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Express the given curve in polar coordinates. Express the given curve in polar coordinates.

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For the parametric curve: x = 4 + 5 cos t, y = 3 + 3 sin t, eliminate the parameter and express in rectangular form.


A) For the parametric curve: x = 4 + 5 cos t, y = 3 + 3 sin t, eliminate the parameter and express in rectangular form. A) B) C) D) E)
B) For the parametric curve: x = 4 + 5 cos t, y = 3 + 3 sin t, eliminate the parameter and express in rectangular form. A) B) C) D) E)
C) For the parametric curve: x = 4 + 5 cos t, y = 3 + 3 sin t, eliminate the parameter and express in rectangular form. A) B) C) D) E)
D) For the parametric curve: x = 4 + 5 cos t, y = 3 + 3 sin t, eliminate the parameter and express in rectangular form. A) B) C) D) E)
E) For the parametric curve: x = 4 + 5 cos t, y = 3 + 3 sin t, eliminate the parameter and express in rectangular form. A) B) C) D) E)

F) B) and C)
G) A) and B)

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Find the ends of the minor axis of the ellipse Find the ends of the minor axis of the ellipse in the x'y'-coordinate system. in the x'y'-coordinate system.

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Create the parametric equation to describe a circle of radius 13 oriented clockwise.

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x = 13 sin...

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Rotate the coordinate axes to remove the xy-term. What is the equation in the new Rotate the coordinate axes to remove the xy-term. What is the equation in the new coordinate system? What type of conic section is it? coordinate system? What type of conic section is it? Rotate the coordinate axes to remove the xy-term. What is the equation in the new coordinate system? What type of conic section is it?

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For the parametric equation x = 2t + 9 , y = 8t - 3 , the value of For the parametric equation x = 2t + 9 , y = 8t - 3 , the value of at t = 4 is A) 2 B) 9 C) 4 D) 3 E) 0 at t = 4 is


A) 2
B) 9
C) 4
D) 3
E) 0

F) C) and D)
G) B) and E)

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Find the foci of the ellipse Find the foci of the ellipse in the x'y'-coordinate system. in the x'y'-coordinate system.

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Identify the conic section by transforming to rectangular coordinates. Identify the conic section by transforming to rectangular coordinates.

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A circle through the...

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Find the area inside the circle Find the area inside the circle , and to the right of the line . , and to the right of the line Find the area inside the circle , and to the right of the line . .

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Find the intersection point(s) of the circle Find the intersection point(s) of the circle and the cardioid for A) B) and C) and D) and E) There are none and the cardioid Find the intersection point(s) of the circle and the cardioid for A) B) and C) and D) and E) There are none for Find the intersection point(s) of the circle and the cardioid for A) B) and C) and D) and E) There are none


A) Find the intersection point(s) of the circle and the cardioid for A) B) and C) and D) and E) There are none
B) Find the intersection point(s) of the circle and the cardioid for A) B) and C) and D) and E) There are none and
Find the intersection point(s) of the circle and the cardioid for A) B) and C) and D) and E) There are none
C) Find the intersection point(s) of the circle and the cardioid for A) B) and C) and D) and E) There are none and
Find the intersection point(s) of the circle and the cardioid for A) B) and C) and D) and E) There are none
D) Find the intersection point(s) of the circle and the cardioid for A) B) and C) and D) and E) There are none and
Find the intersection point(s) of the circle and the cardioid for A) B) and C) and D) and E) There are none
E) There are none

F) None of the above
G) B) and D)

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For the parametric curve: For the parametric curve: , , eliminate the parameter and express in rectangular form. A) x<sup>2</sup> + y<sup>2</sup> = 1 B) C) D) E) , For the parametric curve: , , eliminate the parameter and express in rectangular form. A) x<sup>2</sup> + y<sup>2</sup> = 1 B) C) D) E) , eliminate the parameter and express in rectangular form.


A) x2 + y2 = 1
B) For the parametric curve: , , eliminate the parameter and express in rectangular form. A) x<sup>2</sup> + y<sup>2</sup> = 1 B) C) D) E)
C) For the parametric curve: , , eliminate the parameter and express in rectangular form. A) x<sup>2</sup> + y<sup>2</sup> = 1 B) C) D) E)
D) For the parametric curve: , , eliminate the parameter and express in rectangular form. A) x<sup>2</sup> + y<sup>2</sup> = 1 B) C) D) E)
E) For the parametric curve: , , eliminate the parameter and express in rectangular form. A) x<sup>2</sup> + y<sup>2</sup> = 1 B) C) D) E)

F) C) and E)
G) C) and D)

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Sketch the curve in polar coordinates. Sketch the curve in polar coordinates.

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Express the given curve in polar coordinates. Express the given curve in polar coordinates.

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Rotate the coordinates to remove the xy-term. Then, name the conic. Rotate the coordinates to remove the xy-term. Then, name the conic. A) circle B) hyperbola C) ellipse D) parabola


A) circle
B) hyperbola
C) ellipse
D) parabola

E) All of the above
F) A) and B)

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Sketch the curve in polar coordinates. Sketch the curve in polar coordinates.

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For the parametric curve: x = 4t2, y = 4t, eliminate the parameter and express in rectangular form.


A) For the parametric curve: x = 4t<sup>2</sup>, y = 4t, eliminate the parameter and express in rectangular form. A) B) C) D) E)
B) For the parametric curve: x = 4t<sup>2</sup>, y = 4t, eliminate the parameter and express in rectangular form. A) B) C) D) E)
C) For the parametric curve: x = 4t<sup>2</sup>, y = 4t, eliminate the parameter and express in rectangular form. A) B) C) D) E)
D) For the parametric curve: x = 4t<sup>2</sup>, y = 4t, eliminate the parameter and express in rectangular form. A) B) C) D) E)
E) For the parametric curve: x = 4t<sup>2</sup>, y = 4t, eliminate the parameter and express in rectangular form. A) B) C) D) E)

F) A) and B)
G) A) and C)

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Express the given curve in polar coordinates. Express the given curve in polar coordinates.

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Find the polar equation for the conic that has its focus at the pole and its directrix is Find the polar equation for the conic that has its focus at the pole and its directrix is units above the pole and its eccentricity is . A) B) C) D) E) units above the pole and its eccentricity is Find the polar equation for the conic that has its focus at the pole and its directrix is units above the pole and its eccentricity is . A) B) C) D) E) .


A) Find the polar equation for the conic that has its focus at the pole and its directrix is units above the pole and its eccentricity is . A) B) C) D) E)
B) Find the polar equation for the conic that has its focus at the pole and its directrix is units above the pole and its eccentricity is . A) B) C) D) E)
C) Find the polar equation for the conic that has its focus at the pole and its directrix is units above the pole and its eccentricity is . A) B) C) D) E)
D) Find the polar equation for the conic that has its focus at the pole and its directrix is units above the pole and its eccentricity is . A) B) C) D) E)
E) Find the polar equation for the conic that has its focus at the pole and its directrix is units above the pole and its eccentricity is . A) B) C) D) E)

F) None of the above
G) A) and E)

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Find the polar equation for the conic that has its focus at the pole and its directrix is Find the polar equation for the conic that has its focus at the pole and its directrix is units to the right of the pole and its eccentricity is . A) B) C) D) E) units to the right of the pole and its eccentricity is Find the polar equation for the conic that has its focus at the pole and its directrix is units to the right of the pole and its eccentricity is . A) B) C) D) E) .


A) Find the polar equation for the conic that has its focus at the pole and its directrix is units to the right of the pole and its eccentricity is . A) B) C) D) E)
B) Find the polar equation for the conic that has its focus at the pole and its directrix is units to the right of the pole and its eccentricity is . A) B) C) D) E)
C) Find the polar equation for the conic that has its focus at the pole and its directrix is units to the right of the pole and its eccentricity is . A) B) C) D) E)
D) Find the polar equation for the conic that has its focus at the pole and its directrix is units to the right of the pole and its eccentricity is . A) B) C) D) E)
E) Find the polar equation for the conic that has its focus at the pole and its directrix is units to the right of the pole and its eccentricity is . A) B) C) D) E)

F) A) and C)
G) B) and D)

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Find the area of the region that is common to Find the area of the region that is common to and . and Find the area of the region that is common to and . .

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