Question 1

Find the graph of the following polar equation. 
A) 
 
B)

C)

D)

E)

Accepted Answer

A

Question 2

Find three additional polar representations of the point  given in polar coordinates, using 
A) 
  
B) 
  
C) 
  
D) 
  
E)

Accepted Answer

C

Question 3

Match the graph with its equation. 
A) 
B) 
C) 
D) 
E)

Accepted Answer

B

Question 4

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

C)

D)

E)

Accepted Answer

The answer of Find two sets of polar coordinates with...

Question 5

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

B)

C)

D)

E)

Accepted Answer

The answer of Find an interval for $\theta$ for which...

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)

Accepted Answer

The answer of Find the center and foci of the...

Question 7

Find the rectangular graph of the following polar equation. 
A)

B)

C)

D)

E)

Accepted Answer

The answer of Find the rectangular graph of the following...

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:

Accepted Answer

The answer of Find the vertex and focus of the...

Question 9

Find any zeros of r on the interval  . 
A)zeros: 
B)zeros: 
C)zeros: 
D)zeros: 
E)zeros:

Accepted Answer

The answer of Find any zeros of r on the...

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.

Accepted Answer

The answer of Test the graph of the following equation...

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:

Accepted Answer

The answer of Find the vertices and asymptotes of the...

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:

Accepted Answer

The answer of Find the vertex and focus of the...

Question 13

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

B)

C)

D)

E)

Accepted Answer

The answer of Rotate the axes to eliminate the xy-term...

Question 14

Convert the point from polar coordinates to rectangular coordinates. Round answer to three decimal places, if necessary. 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Convert the point from polar coordinates to...

Question 15

Find the graph of the following polar equation. 
A)

B)

C)

D)

E)

Accepted Answer

The answer of Find the graph of the following polar...

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

Accepted Answer

The standard form of a parabola with its vertex at the origin and a horizontal directrix (x = 5) is $x = 4py$, where $p$ is the distance from the vertex to the directrix. Since the directrix is 5 units away from the origin, $p = -5$ (negative because the parabola opens to the left). Substituting $p = -5$ into the equation gives $x = 4(-5)y = -20y$, which rearranges to $x = 20y$.

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:

Accepted Answer

The answer of Find the center and foci of the...

Question 18

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

B)

C)

D)

E)

Accepted Answer

The answer of Which set of parametric equations represents the...

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

Accepted Answer

The answer of A projectile is launched from ground level...

Quiz 7: Conics and Parametric Equations

Find the graph of the following polar equation.

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

Match the graph with its equation.

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

Find an interval for $\theta$ for which the graph is traced only once. $Find an interval for \theta for which the graph is traced only once. A) B) C) D) E)$

Find the center and foci of the ellipse.

Find the rectangular graph of the following polar equation.

Find the vertex and focus of the parabola below.

Find any zeros of r on the interval .

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

Find the vertices and asymptotes of the hyperbola. $Find the vertices and asymptotes of the hyperbola. A) vertices: (0, \pm 2) asymptote: B) vertices: (0, \pm 2) asymptote: C) vertices: ( \pm 2, 0) asymptote: D) vertices: ( \pm 2, 0) asymptote: E) vertices: ( \pm 2, 3) asymptote:$

Find the vertex and focus of the parabola.

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

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

Find the graph of the following polar equation.

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

Find the center and foci of the following ellipse.

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

Quiz 7: Conics and Parametric Equations

Find the graph of the following polar equation.

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

Match the graph with its equation.

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

Find an interval for θ\thetaθ for which the graph is traced only once.

Find the center and foci of the ellipse.

Find the rectangular graph of the following polar equation.

Find the vertex and focus of the parabola below.

Find any zeros of r on the interval .

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

Find the vertices and asymptotes of the hyperbola.

Find the vertex and focus of the parabola.

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

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

Find the graph of the following polar equation.

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

Find the center and foci of the following ellipse.

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

Find an interval for $\theta$ for which the graph is traced only once. $Find an interval for \theta for which the graph is traced only once. A) B) C) D) E)$

Find the vertices and asymptotes of the hyperbola. $Find the vertices and asymptotes of the hyperbola. A) vertices: (0, \pm 2) asymptote: B) vertices: (0, \pm 2) asymptote: C) vertices: ( \pm 2, 0) asymptote: D) vertices: ( \pm 2, 0) asymptote: E) vertices: ( \pm 2, 3) asymptote:$