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Find the area bounded by the smaller loop of the curve r = 1 + 2 sin( θ\theta ) .


A) 2 π\pi -  Find the area bounded by the smaller loop of the curve r = 1 + 2 sin( \theta ) . A)  2 \pi  -   square units B)  2 \pi  +   square units C)   \pi  -   square units D)   \pi  +   square units E)    -   square units square units
B) 2 π\pi +  Find the area bounded by the smaller loop of the curve r = 1 + 2 sin( \theta ) . A)  2 \pi  -   square units B)  2 \pi  +   square units C)   \pi  -   square units D)   \pi  +   square units E)    -   square units square units
C) π\pi -  Find the area bounded by the smaller loop of the curve r = 1 + 2 sin( \theta ) . A)  2 \pi  -   square units B)  2 \pi  +   square units C)   \pi  -   square units D)   \pi  +   square units E)    -   square units square units
D) π\pi +  Find the area bounded by the smaller loop of the curve r = 1 + 2 sin( \theta ) . A)  2 \pi  -   square units B)  2 \pi  +   square units C)   \pi  -   square units D)   \pi  +   square units E)    -   square units square units
E)  Find the area bounded by the smaller loop of the curve r = 1 + 2 sin( \theta ) . A)  2 \pi  -   square units B)  2 \pi  +   square units C)   \pi  -   square units D)   \pi  +   square units E)    -   square units -  Find the area bounded by the smaller loop of the curve r = 1 + 2 sin( \theta ) . A)  2 \pi  -   square units B)  2 \pi  +   square units C)   \pi  -   square units D)   \pi  +   square units E)    -   square units square units

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Find the equation of the parabola whose focus is (2, -1) and directrix is x + 2y -1 = 0.


A) 4x2 - 4xy + y2 -18x + 14y + 24 = 0
B) 5x2 - 4xy + y2 -18x + 14y + 24 = 0
C) x2 - 4xy + 4y2 -18x + 14y + 24 = 0
D) x2 - 4xy + 5y2 -18x + 14y + 24 = 0
E) 4x2 - 4xy + 4y2 -18x + 14y + 24 = 0

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Find the arc length of r =  Find the arc length of r =     from  \theta  = 0 to  \theta  =   . A)    units B)    units C)    units D)    units E)    units  Find the arc length of r =     from  \theta  = 0 to  \theta  =   . A)    units B)    units C)    units D)    units E)    units from θ\theta = 0 to θ\theta =  Find the arc length of r =     from  \theta  = 0 to  \theta  =   . A)    units B)    units C)    units D)    units E)    units .


A)  Find the arc length of r =     from  \theta  = 0 to  \theta  =   . A)    units B)    units C)    units D)    units E)    units units
B)  Find the arc length of r =     from  \theta  = 0 to  \theta  =   . A)    units B)    units C)    units D)    units E)    units units
C)  Find the arc length of r =     from  \theta  = 0 to  \theta  =   . A)    units B)    units C)    units D)    units E)    units units
D)  Find the arc length of r =     from  \theta  = 0 to  \theta  =   . A)    units B)    units C)    units D)    units E)    units units
E)  Find the arc length of r =     from  \theta  = 0 to  \theta  =   . A)    units B)    units C)    units D)    units E)    units units

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The equations x(t) =  The equations x(t)  =   , y(t)  =   , -1  \le  t  \le  1 are the parametric equations of A)  the whole circle centred at (0 , 0)  and is of radius 1 unit B)  the left half of the circle centred at (0 , 0)  and is of radius 1 unit C)  the bottom half of the circle centred at (0 , 0)  and is of radius 1 unit D)  the top half of the circle centred at (0 , 0)  and is of radius 1 unit E)  the right half of the circle centred at (0 , 0)  and is of radius 1 unit , y(t) =  The equations x(t)  =   , y(t)  =   , -1  \le  t  \le  1 are the parametric equations of A)  the whole circle centred at (0 , 0)  and is of radius 1 unit B)  the left half of the circle centred at (0 , 0)  and is of radius 1 unit C)  the bottom half of the circle centred at (0 , 0)  and is of radius 1 unit D)  the top half of the circle centred at (0 , 0)  and is of radius 1 unit E)  the right half of the circle centred at (0 , 0)  and is of radius 1 unit , -1 \le t \le 1 are the parametric equations of


A) the whole circle centred at (0 , 0) and is of radius 1 unit
B) the left half of the circle centred at (0 , 0) and is of radius 1 unit
C) the bottom half of the circle centred at (0 , 0) and is of radius 1 unit
D) the top half of the circle centred at (0 , 0) and is of radius 1 unit
E) the right half of the circle centred at (0 , 0) and is of radius 1 unit

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Find the length of r =  Find the length of r =   from  \theta  = 0 to  \theta  = 2 \pi . A)    (   - 1)  units B)    (   - 1)  units C)    (   - 1)  units D)  2   (   - 1)  units E)    (   + 1)  units from θ\theta = 0 to θ\theta = 2 π\pi .


A)  Find the length of r =   from  \theta  = 0 to  \theta  = 2 \pi . A)    (   - 1)  units B)    (   - 1)  units C)    (   - 1)  units D)  2   (   - 1)  units E)    (   + 1)  units (  Find the length of r =   from  \theta  = 0 to  \theta  = 2 \pi . A)    (   - 1)  units B)    (   - 1)  units C)    (   - 1)  units D)  2   (   - 1)  units E)    (   + 1)  units - 1) units
B)  Find the length of r =   from  \theta  = 0 to  \theta  = 2 \pi . A)    (   - 1)  units B)    (   - 1)  units C)    (   - 1)  units D)  2   (   - 1)  units E)    (   + 1)  units (  Find the length of r =   from  \theta  = 0 to  \theta  = 2 \pi . A)    (   - 1)  units B)    (   - 1)  units C)    (   - 1)  units D)  2   (   - 1)  units E)    (   + 1)  units - 1) units
C)  Find the length of r =   from  \theta  = 0 to  \theta  = 2 \pi . A)    (   - 1)  units B)    (   - 1)  units C)    (   - 1)  units D)  2   (   - 1)  units E)    (   + 1)  units (  Find the length of r =   from  \theta  = 0 to  \theta  = 2 \pi . A)    (   - 1)  units B)    (   - 1)  units C)    (   - 1)  units D)  2   (   - 1)  units E)    (   + 1)  units - 1) units
D) 2  Find the length of r =   from  \theta  = 0 to  \theta  = 2 \pi . A)    (   - 1)  units B)    (   - 1)  units C)    (   - 1)  units D)  2   (   - 1)  units E)    (   + 1)  units (  Find the length of r =   from  \theta  = 0 to  \theta  = 2 \pi . A)    (   - 1)  units B)    (   - 1)  units C)    (   - 1)  units D)  2   (   - 1)  units E)    (   + 1)  units - 1) units
E)  Find the length of r =   from  \theta  = 0 to  \theta  = 2 \pi . A)    (   - 1)  units B)    (   - 1)  units C)    (   - 1)  units D)  2   (   - 1)  units E)    (   + 1)  units (  Find the length of r =   from  \theta  = 0 to  \theta  = 2 \pi . A)    (   - 1)  units B)    (   - 1)  units C)    (   - 1)  units D)  2   (   - 1)  units E)    (   + 1)  units + 1) units

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Sketch the polar curve r = 4 sin(3θ).

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If x = f( θ\theta ) cos( θ\theta ), y = f( θ\theta ) sin( θ\theta ) for θ\theta  If x = f( \theta ) cos( \theta ), y = f( \theta ) sin( \theta ) for  \theta    [  ,  ] , are parametric equations of a plane curve C, then the equation of curve C in polar coordinates is r = f( \theta ),  \theta  1ee7b17_3372_5854_ae82_d19d2ea0c252_TB9661_11  [  ,  ]. [ If x = f( \theta ) cos( \theta ), y = f( \theta ) sin( \theta ) for  \theta    [  ,  ] , are parametric equations of a plane curve C, then the equation of curve C in polar coordinates is r = f( \theta ),  \theta  1ee7b17_3372_5854_ae82_d19d2ea0c252_TB9661_11  [  ,  ]. ,  If x = f( \theta ) cos( \theta ), y = f( \theta ) sin( \theta ) for  \theta    [  ,  ] , are parametric equations of a plane curve C, then the equation of curve C in polar coordinates is r = f( \theta ),  \theta  1ee7b17_3372_5854_ae82_d19d2ea0c252_TB9661_11  [  ,  ]. ] , are parametric equations of a plane curve C, then the equation of curve C in polar coordinates is r = f( θ\theta ), θ\theta 1ee7b17_3372_5854_ae82_d19d2ea0c252_TB9661_11 [11ee7b18_881f_7ad5_ae82_ef6a0704a9e3_TB9661_11 , 11ee7b18_ef83_6016_ae82_a1fef198316c_TB9661_11].

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Determine the coordinates of the points where the curve x = Determine the coordinates of the points where the curve x =   + 2t, y = 2   + 7 has (a)  a horizontal tangent and (b)  a vertical tangent. A)  (a)  (0, -9)  (b)  (±2, -6)  B)  (a)  (-2, -9)  (b)  (-2, -6)  C)  (a)  (2, -9)  (b)  (2, -6)  D)  (a)  (0, -9)  (b)  (2, 6)  E)  (a)  (2, 9)  (b)  (2, 6) + 2t, y = 2 Determine the coordinates of the points where the curve x =   + 2t, y = 2   + 7 has (a)  a horizontal tangent and (b)  a vertical tangent. A)  (a)  (0, -9)  (b)  (±2, -6)  B)  (a)  (-2, -9)  (b)  (-2, -6)  C)  (a)  (2, -9)  (b)  (2, -6)  D)  (a)  (0, -9)  (b)  (2, 6)  E)  (a)  (2, 9)  (b)  (2, 6) + 7 has (a) a horizontal tangent and (b) a vertical tangent.


A) (a) (0, -9) (b) (±2, -6)
B) (a) (-2, -9) (b) (-2, -6)
C) (a) (2, -9) (b) (2, -6)
D) (a) (0, -9) (b) (2, 6)
E) (a) (2, 9) (b) (2, 6)

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Find the arc length x = 2 cos θ\theta + cos 2 θ\theta + 1, y = 2 sin θ\theta + sin 2 θ\theta , for 0 \le θ\theta\le 2 π\pi .


A) 12 units
B) 14 units
C) 16 units
D) 18 units
E) 10 units

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Find the Cartesian equation of the straight line tangent to the plane curve given parametrically by Find the Cartesian equation of the straight line tangent to the plane curve given parametrically by   at the point on the curve where t = -1. A)  x + y = 0 B)  3x - y =0 C)  y = 0 D)  y =   x E)  y = -3x at the point on the curve where t = -1.


A) x + y = 0
B) 3x - y =0
C) y = 0
D) y = Find the Cartesian equation of the straight line tangent to the plane curve given parametrically by   at the point on the curve where t = -1. A)  x + y = 0 B)  3x - y =0 C)  y = 0 D)  y =   x E)  y = -3x x
E) y = -3x

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The equation of a conic section in polar coordinates is given by r = The equation of a conic section in polar coordinates is given by r =   .(i) Transform the equation of the conic section to rectangular coordinates (x , y).(ii) Identify the conic section. .(i) Transform the equation of the conic section to rectangular coordinates (x , y).(ii) Identify the conic section.

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Find g(t) so that x = -1 + 3 cos(t) , y = g(t) , 0 \le t \le 2 π\pi provides a counterclockwise parametrization of the circle  Find g(t)  so that x = -1 + 3 cos(t) , y = g(t) , 0 \le  t  \le  2 \pi  provides a counterclockwise parametrization of the circle   +   + 2x - 4y = 4. A)  -2 + sin(t)  B)  2 - 3 sin(t)  C)  2 + 3 sin(t)  D)  3 - 2 sin(t)  E)  3 + 2 sin(t)  +  Find g(t)  so that x = -1 + 3 cos(t) , y = g(t) , 0 \le  t  \le  2 \pi  provides a counterclockwise parametrization of the circle   +   + 2x - 4y = 4. A)  -2 + sin(t)  B)  2 - 3 sin(t)  C)  2 + 3 sin(t)  D)  3 - 2 sin(t)  E)  3 + 2 sin(t)  + 2x - 4y = 4.


A) -2 + sin(t)
B) 2 - 3 sin(t)
C) 2 + 3 sin(t)
D) 3 - 2 sin(t)
E) 3 + 2 sin(t)

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Convert the point with Cartesian coordinates (-1, -1) to polar coordinates.


A) Convert the point with Cartesian coordinates (-1, -1)  to polar coordinates. A)    B)    C)    D)    E)
B) Convert the point with Cartesian coordinates (-1, -1)  to polar coordinates. A)    B)    C)    D)    E)
C) Convert the point with Cartesian coordinates (-1, -1)  to polar coordinates. A)    B)    C)    D)    E)
D) Convert the point with Cartesian coordinates (-1, -1)  to polar coordinates. A)    B)    C)    D)    E)
E) Convert the point with Cartesian coordinates (-1, -1)  to polar coordinates. A)    B)    C)    D)    E)

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For the parabola For the parabola   + 6x + 4y + 5 = 0, find the vertex, the focus, and the directrix. A)  Vertex (3, 1) , Focus (3, 2) , Directrix y = 0 B)  Vertex (3, 1) , Focus (3, 0) , Directrix y = 2 C)  Vertex (-3, 1) , Focus (-3, 2) , Directrix y = 0 D)  Vertex (-3, 1) , Focus (-3, 0) , Directrix y = 2 E)  Vertex (-3, -1) , Focus (-3, 0) , Directrix y = 2 + 6x + 4y + 5 = 0, find the vertex, the focus, and the directrix.


A) Vertex (3, 1) , Focus (3, 2) , Directrix y = 0
B) Vertex (3, 1) , Focus (3, 0) , Directrix y = 2
C) Vertex (-3, 1) , Focus (-3, 2) , Directrix y = 0
D) Vertex (-3, 1) , Focus (-3, 0) , Directrix y = 2
E) Vertex (-3, -1) , Focus (-3, 0) , Directrix y = 2

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Transform the polar equation r = 1 + 2 cos θ\theta to rectangular coordinates.


A)  Transform the polar equation r = 1 + 2 cos  \theta  to rectangular coordinates. A)    +   =   B)    +   =   C)    -   =   D)    +   =   E)    -   =   +  Transform the polar equation r = 1 + 2 cos  \theta  to rectangular coordinates. A)    +   =   B)    +   =   C)    -   =   D)    +   =   E)    -   =   =  Transform the polar equation r = 1 + 2 cos  \theta  to rectangular coordinates. A)    +   =   B)    +   =   C)    -   =   D)    +   =   E)    -   =
B)  Transform the polar equation r = 1 + 2 cos  \theta  to rectangular coordinates. A)    +   =   B)    +   =   C)    -   =   D)    +   =   E)    -   =   +  Transform the polar equation r = 1 + 2 cos  \theta  to rectangular coordinates. A)    +   =   B)    +   =   C)    -   =   D)    +   =   E)    -   =   =  Transform the polar equation r = 1 + 2 cos  \theta  to rectangular coordinates. A)    +   =   B)    +   =   C)    -   =   D)    +   =   E)    -   =
C)  Transform the polar equation r = 1 + 2 cos  \theta  to rectangular coordinates. A)    +   =   B)    +   =   C)    -   =   D)    +   =   E)    -   =   -  Transform the polar equation r = 1 + 2 cos  \theta  to rectangular coordinates. A)    +   =   B)    +   =   C)    -   =   D)    +   =   E)    -   =   =  Transform the polar equation r = 1 + 2 cos  \theta  to rectangular coordinates. A)    +   =   B)    +   =   C)    -   =   D)    +   =   E)    -   =
D)  Transform the polar equation r = 1 + 2 cos  \theta  to rectangular coordinates. A)    +   =   B)    +   =   C)    -   =   D)    +   =   E)    -   =   +  Transform the polar equation r = 1 + 2 cos  \theta  to rectangular coordinates. A)    +   =   B)    +   =   C)    -   =   D)    +   =   E)    -   =   =  Transform the polar equation r = 1 + 2 cos  \theta  to rectangular coordinates. A)    +   =   B)    +   =   C)    -   =   D)    +   =   E)    -   =
E)  Transform the polar equation r = 1 + 2 cos  \theta  to rectangular coordinates. A)    +   =   B)    +   =   C)    -   =   D)    +   =   E)    -   =   -  Transform the polar equation r = 1 + 2 cos  \theta  to rectangular coordinates. A)    +   =   B)    +   =   C)    -   =   D)    +   =   E)    -   =   =  Transform the polar equation r = 1 + 2 cos  \theta  to rectangular coordinates. A)    +   =   B)    +   =   C)    -   =   D)    +   =   E)    -   =

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A conic section is given by the equation 4x2 + 10xy + 4y2 = 36.Use rotation of coordinate axes through an appropriate acute angle θ\theta to find the new equation of the conic section in the uv-coordinate axes , where x = u cos( θ\theta ) - v sin( θ\theta ) , y = u sin( θ\theta ) + v cos( θ\theta ) . Then identify the conic section.


A)  A conic section is given by the equation 4x<sup>2</sup> + 10xy + 4y<sup>2</sup> = 36.Use rotation of coordinate axes through an appropriate acute angle  \theta  to find the new equation of the conic section in the uv-coordinate axes , where x = u cos( \theta )  - v sin( \theta )  , y = u sin( \theta )  + v cos( \theta ) . Then identify the conic section. A)    +   = 1, an ellipse B)    +   = 4, a circle C)    -   = 1, a hyperbola D)    +   = 1, an ellipse E)    -   = 1, a hyperbola +  A conic section is given by the equation 4x<sup>2</sup> + 10xy + 4y<sup>2</sup> = 36.Use rotation of coordinate axes through an appropriate acute angle  \theta  to find the new equation of the conic section in the uv-coordinate axes , where x = u cos( \theta )  - v sin( \theta )  , y = u sin( \theta )  + v cos( \theta ) . Then identify the conic section. A)    +   = 1, an ellipse B)    +   = 4, a circle C)    -   = 1, a hyperbola D)    +   = 1, an ellipse E)    -   = 1, a hyperbola = 1, an ellipse
B)  A conic section is given by the equation 4x<sup>2</sup> + 10xy + 4y<sup>2</sup> = 36.Use rotation of coordinate axes through an appropriate acute angle  \theta  to find the new equation of the conic section in the uv-coordinate axes , where x = u cos( \theta )  - v sin( \theta )  , y = u sin( \theta )  + v cos( \theta ) . Then identify the conic section. A)    +   = 1, an ellipse B)    +   = 4, a circle C)    -   = 1, a hyperbola D)    +   = 1, an ellipse E)    -   = 1, a hyperbola +  A conic section is given by the equation 4x<sup>2</sup> + 10xy + 4y<sup>2</sup> = 36.Use rotation of coordinate axes through an appropriate acute angle  \theta  to find the new equation of the conic section in the uv-coordinate axes , where x = u cos( \theta )  - v sin( \theta )  , y = u sin( \theta )  + v cos( \theta ) . Then identify the conic section. A)    +   = 1, an ellipse B)    +   = 4, a circle C)    -   = 1, a hyperbola D)    +   = 1, an ellipse E)    -   = 1, a hyperbola = 4, a circle
C)  A conic section is given by the equation 4x<sup>2</sup> + 10xy + 4y<sup>2</sup> = 36.Use rotation of coordinate axes through an appropriate acute angle  \theta  to find the new equation of the conic section in the uv-coordinate axes , where x = u cos( \theta )  - v sin( \theta )  , y = u sin( \theta )  + v cos( \theta ) . Then identify the conic section. A)    +   = 1, an ellipse B)    +   = 4, a circle C)    -   = 1, a hyperbola D)    +   = 1, an ellipse E)    -   = 1, a hyperbola -  A conic section is given by the equation 4x<sup>2</sup> + 10xy + 4y<sup>2</sup> = 36.Use rotation of coordinate axes through an appropriate acute angle  \theta  to find the new equation of the conic section in the uv-coordinate axes , where x = u cos( \theta )  - v sin( \theta )  , y = u sin( \theta )  + v cos( \theta ) . Then identify the conic section. A)    +   = 1, an ellipse B)    +   = 4, a circle C)    -   = 1, a hyperbola D)    +   = 1, an ellipse E)    -   = 1, a hyperbola = 1, a hyperbola
D)  A conic section is given by the equation 4x<sup>2</sup> + 10xy + 4y<sup>2</sup> = 36.Use rotation of coordinate axes through an appropriate acute angle  \theta  to find the new equation of the conic section in the uv-coordinate axes , where x = u cos( \theta )  - v sin( \theta )  , y = u sin( \theta )  + v cos( \theta ) . Then identify the conic section. A)    +   = 1, an ellipse B)    +   = 4, a circle C)    -   = 1, a hyperbola D)    +   = 1, an ellipse E)    -   = 1, a hyperbola +  A conic section is given by the equation 4x<sup>2</sup> + 10xy + 4y<sup>2</sup> = 36.Use rotation of coordinate axes through an appropriate acute angle  \theta  to find the new equation of the conic section in the uv-coordinate axes , where x = u cos( \theta )  - v sin( \theta )  , y = u sin( \theta )  + v cos( \theta ) . Then identify the conic section. A)    +   = 1, an ellipse B)    +   = 4, a circle C)    -   = 1, a hyperbola D)    +   = 1, an ellipse E)    -   = 1, a hyperbola = 1, an ellipse
E)  A conic section is given by the equation 4x<sup>2</sup> + 10xy + 4y<sup>2</sup> = 36.Use rotation of coordinate axes through an appropriate acute angle  \theta  to find the new equation of the conic section in the uv-coordinate axes , where x = u cos( \theta )  - v sin( \theta )  , y = u sin( \theta )  + v cos( \theta ) . Then identify the conic section. A)    +   = 1, an ellipse B)    +   = 4, a circle C)    -   = 1, a hyperbola D)    +   = 1, an ellipse E)    -   = 1, a hyperbola -  A conic section is given by the equation 4x<sup>2</sup> + 10xy + 4y<sup>2</sup> = 36.Use rotation of coordinate axes through an appropriate acute angle  \theta  to find the new equation of the conic section in the uv-coordinate axes , where x = u cos( \theta )  - v sin( \theta )  , y = u sin( \theta )  + v cos( \theta ) . Then identify the conic section. A)    +   = 1, an ellipse B)    +   = 4, a circle C)    -   = 1, a hyperbola D)    +   = 1, an ellipse E)    -   = 1, a hyperbola = 1, a hyperbola

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Find an equation of a parabola satisfying the given conditions: Focus (2, 0) and directrix y = 2?.


A)  Find an equation of a parabola satisfying the given conditions: Focus (2, 0)  and directrix y = 2?. A)    = 4  \pi (1 - y)  B)    = 4(  \pi  - y)  C)    = 4  \pi (  \pi  - y)  D)    = 4  \pi (  \pi  - y)  E)    = 4  \pi (  \pi  - y)  = 4 π\pi (1 - y)
B)  Find an equation of a parabola satisfying the given conditions: Focus (2, 0)  and directrix y = 2?. A)    = 4  \pi (1 - y)  B)    = 4(  \pi  - y)  C)    = 4  \pi (  \pi  - y)  D)    = 4  \pi (  \pi  - y)  E)    = 4  \pi (  \pi  - y)  = 4( π\pi - y)
C)  Find an equation of a parabola satisfying the given conditions: Focus (2, 0)  and directrix y = 2?. A)    = 4  \pi (1 - y)  B)    = 4(  \pi  - y)  C)    = 4  \pi (  \pi  - y)  D)    = 4  \pi (  \pi  - y)  E)    = 4  \pi (  \pi  - y)  = 4 π\pi ( π\pi - y)
D)  Find an equation of a parabola satisfying the given conditions: Focus (2, 0)  and directrix y = 2?. A)    = 4  \pi (1 - y)  B)    = 4(  \pi  - y)  C)    = 4  \pi (  \pi  - y)  D)    = 4  \pi (  \pi  - y)  E)    = 4  \pi (  \pi  - y)  = 4 π\pi ( π\pi - y)
E)  Find an equation of a parabola satisfying the given conditions: Focus (2, 0)  and directrix y = 2?. A)    = 4  \pi (1 - y)  B)    = 4(  \pi  - y)  C)    = 4  \pi (  \pi  - y)  D)    = 4  \pi (  \pi  - y)  E)    = 4  \pi (  \pi  - y)  = 4 π\pi ( π\pi - y)

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Find the area bounded by the polar curve r = sin(3 θ\theta ) .


A)  Find the area bounded by the polar curve r = sin(3 \theta ) . A)    square units B)    square units C)    square units D)    square units E)    square units square units
B)  Find the area bounded by the polar curve r = sin(3 \theta ) . A)    square units B)    square units C)    square units D)    square units E)    square units square units
C)  Find the area bounded by the polar curve r = sin(3 \theta ) . A)    square units B)    square units C)    square units D)    square units E)    square units square units
D)  Find the area bounded by the polar curve r = sin(3 \theta ) . A)    square units B)    square units C)    square units D)    square units E)    square units square units
E)  Find the area bounded by the polar curve r = sin(3 \theta ) . A)    square units B)    square units C)    square units D)    square units E)    square units square units

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Express  Express   and   in terms of x and y for the circle x = a cos \theta  , y = a sin  \theta  . A)    = -   ,   = -   B)    =   ,   =   C)    = -   ,   = -   D)    =   ,   = -   E)    =   ,   = -   and  Express   and   in terms of x and y for the circle x = a cos \theta  , y = a sin  \theta  . A)    = -   ,   = -   B)    =   ,   =   C)    = -   ,   = -   D)    =   ,   = -   E)    =   ,   = -   in terms of x and y for the circle x = a cos θ\theta , y = a sin θ\theta .


A)  Express   and   in terms of x and y for the circle x = a cos \theta  , y = a sin  \theta  . A)    = -   ,   = -   B)    =   ,   =   C)    = -   ,   = -   D)    =   ,   = -   E)    =   ,   = -   = -  Express   and   in terms of x and y for the circle x = a cos \theta  , y = a sin  \theta  . A)    = -   ,   = -   B)    =   ,   =   C)    = -   ,   = -   D)    =   ,   = -   E)    =   ,   = -   ,  Express   and   in terms of x and y for the circle x = a cos \theta  , y = a sin  \theta  . A)    = -   ,   = -   B)    =   ,   =   C)    = -   ,   = -   D)    =   ,   = -   E)    =   ,   = -   = -  Express   and   in terms of x and y for the circle x = a cos \theta  , y = a sin  \theta  . A)    = -   ,   = -   B)    =   ,   =   C)    = -   ,   = -   D)    =   ,   = -   E)    =   ,   = -
B)  Express   and   in terms of x and y for the circle x = a cos \theta  , y = a sin  \theta  . A)    = -   ,   = -   B)    =   ,   =   C)    = -   ,   = -   D)    =   ,   = -   E)    =   ,   = -   =  Express   and   in terms of x and y for the circle x = a cos \theta  , y = a sin  \theta  . A)    = -   ,   = -   B)    =   ,   =   C)    = -   ,   = -   D)    =   ,   = -   E)    =   ,   = -   ,  Express   and   in terms of x and y for the circle x = a cos \theta  , y = a sin  \theta  . A)    = -   ,   = -   B)    =   ,   =   C)    = -   ,   = -   D)    =   ,   = -   E)    =   ,   = -   =  Express   and   in terms of x and y for the circle x = a cos \theta  , y = a sin  \theta  . A)    = -   ,   = -   B)    =   ,   =   C)    = -   ,   = -   D)    =   ,   = -   E)    =   ,   = -
C)  Express   and   in terms of x and y for the circle x = a cos \theta  , y = a sin  \theta  . A)    = -   ,   = -   B)    =   ,   =   C)    = -   ,   = -   D)    =   ,   = -   E)    =   ,   = -   = -  Express   and   in terms of x and y for the circle x = a cos \theta  , y = a sin  \theta  . A)    = -   ,   = -   B)    =   ,   =   C)    = -   ,   = -   D)    =   ,   = -   E)    =   ,   = -   ,  Express   and   in terms of x and y for the circle x = a cos \theta  , y = a sin  \theta  . A)    = -   ,   = -   B)    =   ,   =   C)    = -   ,   = -   D)    =   ,   = -   E)    =   ,   = -   = -  Express   and   in terms of x and y for the circle x = a cos \theta  , y = a sin  \theta  . A)    = -   ,   = -   B)    =   ,   =   C)    = -   ,   = -   D)    =   ,   = -   E)    =   ,   = -
D)  Express   and   in terms of x and y for the circle x = a cos \theta  , y = a sin  \theta  . A)    = -   ,   = -   B)    =   ,   =   C)    = -   ,   = -   D)    =   ,   = -   E)    =   ,   = -   =  Express   and   in terms of x and y for the circle x = a cos \theta  , y = a sin  \theta  . A)    = -   ,   = -   B)    =   ,   =   C)    = -   ,   = -   D)    =   ,   = -   E)    =   ,   = -   ,  Express   and   in terms of x and y for the circle x = a cos \theta  , y = a sin  \theta  . A)    = -   ,   = -   B)    =   ,   =   C)    = -   ,   = -   D)    =   ,   = -   E)    =   ,   = -   = -  Express   and   in terms of x and y for the circle x = a cos \theta  , y = a sin  \theta  . A)    = -   ,   = -   B)    =   ,   =   C)    = -   ,   = -   D)    =   ,   = -   E)    =   ,   = -
E)  Express   and   in terms of x and y for the circle x = a cos \theta  , y = a sin  \theta  . A)    = -   ,   = -   B)    =   ,   =   C)    = -   ,   = -   D)    =   ,   = -   E)    =   ,   = -   =  Express   and   in terms of x and y for the circle x = a cos \theta  , y = a sin  \theta  . A)    = -   ,   = -   B)    =   ,   =   C)    = -   ,   = -   D)    =   ,   = -   E)    =   ,   = -   ,  Express   and   in terms of x and y for the circle x = a cos \theta  , y = a sin  \theta  . A)    = -   ,   = -   B)    =   ,   =   C)    = -   ,   = -   D)    =   ,   = -   E)    =   ,   = -   = -  Express   and   in terms of x and y for the circle x = a cos \theta  , y = a sin  \theta  . A)    = -   ,   = -   B)    =   ,   =   C)    = -   ,   = -   D)    =   ,   = -   E)    =   ,   = -

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What are the polar coordinates of the highest point on the cardioid r = 2(1 + cos θ\theta ) ?


A)  What are the polar coordinates of the highest point on the cardioid r = 2(1 + cos  \theta ) ? A)    B)    C)    D)  (4, 0)  E)
B)  What are the polar coordinates of the highest point on the cardioid r = 2(1 + cos  \theta ) ? A)    B)    C)    D)  (4, 0)  E)
C)  What are the polar coordinates of the highest point on the cardioid r = 2(1 + cos  \theta ) ? A)    B)    C)    D)  (4, 0)  E)
D) (4, 0)
E)  What are the polar coordinates of the highest point on the cardioid r = 2(1 + cos  \theta ) ? A)    B)    C)    D)  (4, 0)  E)

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