Question 1

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

Accepted Answer

A) 
   
B)  
  
C)  
  
D)  
  
E)  
  
A) 
   
B)  
  
C)  
  
D)  
  
E)  
  A

Question 2

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

Accepted Answer

A)  
      
B)  
      
C)  
      
D)  
      
E)  
      
A)  
      
B)  
      
C)  
      
D)  
      
E)  
      C

Question 3

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.   ,

Accepted Answer

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 
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 C

Question 4

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

Accepted Answer

A)  
  
B)  
  
C)  
  
D)  
  
E)  
  
A)  
  
B)  
  
C)  
  
D)  
  
E)

Question 5

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

Accepted Answer

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. 
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 6

Match the graph with its equation.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 7

Find the graph of the following polar equation.

Accepted Answer

A)    
B)  
  
C)    
D)     
E)    
A)    
B)  
  
C)    
D)     
E)

Question 8

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

Accepted Answer

A)  
  
B)  
  
C)  
  
D)  
  
E)  
  
A)  
  
B)  
  
C)  
  
D)  
  
E)

Question 9

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

Accepted Answer

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

Question 10

Find the rectangular graph of the following polar equation.

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
E) 
  
A) 
  
B) 
  
C) 
  
D) 
  
E)

Question 11

Find the vertex and focus of the parabola.

Accepted Answer

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:   
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 12

Find the vertex and focus of the parabola below.

Accepted Answer

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

Question 13

Find any zeros of r on the interval   .

Accepted Answer

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

Question 14

Find the center and foci of the ellipse.

Accepted Answer

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) 
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 15

Find the center and foci of the following ellipse.

Accepted Answer

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

Question 16

Find the graph of the following polar equation.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 17

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

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 18

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

Accepted Answer

A)  
  
B)  
  
C)  
  
D)  
  
E)  
  
A)  
  
B)  
  
C)  
  
D)  
  
E)

Question 19

Find the vertices and asymptotes of the hyperbola.

Accepted Answer

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

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

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

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

Match the graph with its equation.

Find the graph of the following polar equation.

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

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

Find the rectangular graph of the following polar equation.

Find the vertex and focus of the parabola.

Find the vertex and focus of the parabola below.

Find any zeros of r on the interval .

Find the center and foci of the ellipse.

Find the center and foci of the following ellipse.

Find the graph of the following polar equation.

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

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

Find the vertices and asymptotes of the hyperbola.

Functions and Their Graphs

Solving Equations and Inequalities

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Linear Systems and Matrices

Sequences, Series, and Probability

Prerequisites

Filters

Exam 7: Conics and Parametric Equations

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

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

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

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

Match the graph with its equation.

Find the graph of the following polar equation.

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

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

Find the rectangular graph of the following polar equation.

Find the vertex and focus of the parabola.

Find the vertex and focus of the parabola below.

Find any zeros of r on the interval .

Find the center and foci of the ellipse.

Find the center and foci of the following ellipse.

Find the graph of the following polar equation.

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

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

Find the vertices and asymptotes of the hyperbola.

Functions and Their Graphs

Solving Equations and Inequalities

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Linear Systems and Matrices

Sequences, Series, and Probability

Prerequisites

Filters

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