Deck 7: Conics and Parametric Equations

Question 1

Find the graph of the following polar equation.

A)

B)


C)

D)

E)

Answer 1

Question 2

Find three additional polar representations of the point given in polar coordinates, using

A)

B)

C)

D)

E)

Answer 2

Question 3

Match the graph with its equation.

A)
B)
C)
D)
E)

Answer 3

Question 4

Find two sets of polar coordinates with for the point given in rectangular coordinates.

A)

B)

C)

D)

E)

Question 5

Find an interval for $\theta$ for which the graph is traced only once.

A)

B)

C)

D)

E)

Question 6

Find the center and foci of the ellipse.

A)center: (-9, 5) foci: (-9, 3), (-9, 7)
B)center: (9, -5) foci: (9, -7), (9, -3)
C)center: (9, -5) foci: (7, -5), (11, -5)
D)center: (-9, 5) foci: (-11, -5), (-7, -5)
E)center: (9, -5) foci: (-11, 5), (-7, 5)

Question 7

Find the rectangular graph of the following polar equation.

A)

B)

C)

D)

E)

Question 8

Find the vertex and focus of the parabola below.

A)Vertex: Focus:
B)Vertex: Focus:
C)Vertex: Focus:
D)Vertex: Focus:
E)Vertex: Focus:

Question 9

Find any zeros of r on the interval .

A)zeros:
B)zeros:
C)zeros:
D)zeros:
E)zeros:

Question 10

Test the graph of the following equation for symmetry with respect to the polar axis, and the pole.

A)The graph is symmetric with respect to only.
B)The graph is symmetric with respect to the polar axis only.
C)The graph is symmetric with respect to the pole only.
D)The graph is symmetric with respect to all three.
E)The graph has no symmetries.

Question 11

Find the vertices and asymptotes of the hyperbola.

A)vertices: (0, $\pm$ 2) asymptote:
B)vertices: (0, $\pm$ 2) asymptote:
C)vertices: ( $\pm$ 2, 0) asymptote:
D)vertices: ( $\pm$ 2, 0) asymptote:
E)vertices: ( $\pm$ 2, 3) asymptote:

Question 12

Find the vertex and focus of the parabola.

A)vertex: focus: (0, 0)
B)vertex: focus: (0, 0)
C)vertex: (0, 0) focus:
D)vertex: (0, 0) focus:
E)vertex: (0, 0) focus:

Question 13

Rotate the axes to eliminate the xy-term in the following equation.

A)

B)

C)

D)

E)

Question 14

Convert the point from polar coordinates to rectangular coordinates. Round answer to three decimal places, if necessary.

A)
B)
C)
D)
E)

Question 15

Find the graph of the following polar equation.

A)

B)

C)

D)

E)

Question 16

Find the standard form of the parabola with the given characteristic and vertex at the origin. directrix: x = 5

A)x² = -20y
B)x² = 20y
C)x² = 5y
D)y² = 5x
E)y² = -20x

Question 17

Find the center and foci of the following ellipse.

A)Center: Foci:
B)Center: Foci:
C)Center: Foci:
D)Center: Foci:
E)Center: Foci:

Question 18

Which set of parametric equations represents the following line or conic? Use and .
Hyperbola: vertices foci

A)

B)

C)

D)

E)

Question 19

A projectile is launched from ground level at an angle of $\theta$ with the horizontal. The initial velocity is feet per second and the path of the projectile is modeled by the parametric equations and . Use a graphing utility to graph the paths of a projectile launched from ground level with the values given for $\theta$ and . Use the graph to approximate the maximum height and range of the projectile to the nearest foot. ,

A)maximum height $\approx$ 49 feet range $\approx$ 4 feet
B)maximum height $\approx$ 4 feet range $\approx$ 49 feet
C)maximum height $\approx$ 33 feet range $\approx$ 92 feet
D)maximum height $\approx$ 92 feet range $\approx$ 33 feet
E)maximum height $\approx$ 43 feet range $\approx$ 8 feet