Question 1

Identify the graph for the polar equation   .

Accepted Answer

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

Question 2

Identify the conic for the polar equation   when   .

Accepted Answer

A)  hyperbola 
B)  parabola 
C)  ellipse 
A)  hyperbola 
B)  parabola 
C)  ellipse A

Question 3

Find the eccentricity of the polar equation   .

Accepted Answer

A)  78 
B)    
C)  26 
D)  13 
E)    
A)  78 
B)    
C)  26 
D)  13 
E)    B

Question 4

Find a polar equation for the ellipse with its focus at the pole and vertices   .

Accepted Answer

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

Question 5

Find the eccentricity of the polar equation   .

Accepted Answer

A)  28 
B)  14 
C)    
D)    
E)  7 
A)  28 
B)  14 
C)    
D)    
E)  7

Question 6

Identify the graph for the polar equation   .

Accepted Answer

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

Question 7

Find a polar equation for the ellipse with its focus at the pole, eccentricity   , and directrix   .

Accepted Answer

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

Question 8

Find a polar equation for the hyperbola with its focus at the pole, eccentricity   , and directrix   .

Accepted Answer

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

Question 9

Pluto moves in an elliptical orbit with the sun at one of the foci. The length of half of the major axis is   kilometers, and the eccentricity is 0.2488. Find the perihelion distance of Pluto from the sun. Round your answer to the nearest kilometers.

Accepted Answer

A)  8,873,174,401 kilometers 
B)  7,375,412,800 kilometers 
C)  4,436,587,201 kilometers 
D)  4,436,587,200 kilometers 
E)  8,873,174,399 kilometers 
A)  8,873,174,401 kilometers 
B)  7,375,412,800 kilometers 
C)  4,436,587,201 kilometers 
D)  4,436,587,200 kilometers 
E)  8,873,174,399 kilometers

Question 10

Find the distance from the pole to the directrix for the conic   .

Accepted Answer

A)    
B)  14 
C)    
D)  42 
E)  7 
A)    
B)  14 
C)    
D)  42 
E)  7

Question 11

Find the eccentricity and distance from the pole to the directrix of the conic. Then sketch and identify the graph. Use a graphing utility to confirm your results.

Accepted Answer

A)  eccentricity:  
Distance from pole to directrix:  
The graph is an ellipse.   
B)  eccentricity:  
Distance from pole to directrix:  
The graph is a hyperbola.   
C)  eccentricity:  
Distance from pole to directrix:  
The graph is a hyperbola.   
D)  eccentricity:  
Distance from pole to directrix:  
The graph is an ellipse.   
E)  eccentricity:  
Distance from pole to directrix:  
The graph is an ellipse.   
A)  eccentricity:  
Distance from pole to directrix:  
The graph is an ellipse.   
B)  eccentricity:  
Distance from pole to directrix:  
The graph is a hyperbola.   
C)  eccentricity:  
Distance from pole to directrix:  
The graph is a hyperbola.   
D)  eccentricity:  
Distance from pole to directrix:  
The graph is an ellipse.   
E)  eccentricity:  
Distance from pole to directrix:  
The graph is an ellipse.

Question 12

Find a polar equation for the parabola with its focus at the pole, eccentricity e = 1, and directrix   .

Accepted Answer

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

Question 13

Find a polar equation for the parabola with its focus at the pole and vertex   .

Accepted Answer

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

Question 14

Identify the graph for the polar equation   .

Accepted Answer

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

Question 15

Find the eccentricity and distance from the pole to the directrix of the conic. Then sketch and identify the graph. Use a graphing utility to confirm your results.

Accepted Answer

A)  eccentricity:  
Distance from pole to directrix:  
The graph is an ellipse.   
B)  eccentricity: 3
Distance from pole to directrix:  
The graph is an ellipse.   
C)  eccentricity:  
Distance from pole to directrix:  
The graph is an ellipse.   
D)  eccentricity: 3
Distance from pole to directrix:  
The graph is a hyperbola.   
E)  eccentricity: 3
Distance from pole to directrix:  
The graph is a hyperbola.   
A)  eccentricity:  
Distance from pole to directrix:  
The graph is an ellipse.   
B)  eccentricity: 3
Distance from pole to directrix:  
The graph is an ellipse.   
C)  eccentricity:  
Distance from pole to directrix:  
The graph is an ellipse.   
D)  eccentricity: 3
Distance from pole to directrix:  
The graph is a hyperbola.   
E)  eccentricity: 3
Distance from pole to directrix:  
The graph is a hyperbola.

Question 16

Find the distance from the pole to the directrix for the conic   .

Accepted Answer

A)    
B)    
C)  30 
D)    
E)  62 
A)    
B)    
C)  30 
D)    
E)  62

Question 17

Find the distance from the pole to the directrix for the conic   .

Accepted Answer

A)    
B)  32 
C)  16 
D)    
E)  8 
A)    
B)  32 
C)  16 
D)    
E)  8

Question 18

Find the eccentricity of the polar equation   .

Accepted Answer

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

Question 19

Find a polar equation for the hyperbola with its focus at the pole and vertices   .

Accepted Answer

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

Exam 10: Section 6: Conics, Parametric Equations, and Polar Coordinates

Identify the graph for the polar equation .

Identify the conic for the polar equation when .

Find the eccentricity of the polar equation .

Find a polar equation for the ellipse with its focus at the pole and vertices .

Find the eccentricity of the polar equation .

Identify the graph for the polar equation .

Find a polar equation for the ellipse with its focus at the pole, eccentricity , and directrix .

Find a polar equation for the hyperbola with its focus at the pole, eccentricity , and directrix .

Pluto moves in an elliptical orbit with the sun at one of the foci. The length of half of the major axis is kilometers, and the eccentricity is 0.2488. Find the perihelion distance of Pluto from the sun. Round your answer to the nearest kilometers.

Find the distance from the pole to the directrix for the conic .

Find the eccentricity and distance from the pole to the directrix of the conic. Then sketch and identify the graph. Use a graphing utility to confirm your results.

Find a polar equation for the parabola with its focus at the pole, eccentricity e = 1, and directrix .

Find a polar equation for the parabola with its focus at the pole and vertex .

Identify the graph for the polar equation .

Find the eccentricity and distance from the pole to the directrix of the conic. Then sketch and identify the graph. Use a graphing utility to confirm your results.

Find the distance from the pole to the directrix for the conic .

Find the distance from the pole to the directrix for the conic .

Find the eccentricity of the polar equation .

Find a polar equation for the hyperbola with its focus at the pole and vertices .

Section 1: Preparation for Calculus

Section 2: Preparation for Calculus

Section 3: Preparation for Calculus

Section 4: Preparation for Calculus

Section 5: Preparation for Calculus

Section 6: Preparation for Calculus

Section 1: Limits and Their Properties

Section 2: Limits and Their Properties

Section 3: Limits and Their Properties

Section 4: Limits and Their Properties

Section 5 : Limits and Their Properties

Section 1 : Differentiation

Section 2: Differentiation

Section 3: Differentiation

Section 4 : Differentiation

Section 5: Differentiation

Section 6: Differentiation

Section 7: Differentiation

Section 8: Differentiation

Section 1 : Applications of Differentiation

Section 2: Applications of Differentiation

Section 3: Applications of Differentiation

Section 4: Applications of Differentiation

Section 5: Applications of Differentiation

Section 6: Applications of Differentiation

Section 7: Applications of Differentiation

Section 8: Applications of Differentiation

Section 1: Integration

Section 2: Integration

Section 3: Integration

Section 4: Integration

Section 5: Integration

Section 6: Integration

Section 7: Integration

Section 8: Integration

Section 9: Integration

Section 1: Differential Equations

Section 2: Differential Equations

Section 3: Differential Equations

Section 4: Differential Equations

Section 5: Differential Equations

Section 1: Applications of Integration

Section 2: Applications of Integration

Section 3: Applications of Integration

Section 4: Applications of Integration

Section 5: Applications of Integration

Section 6: Applications of Integration

Section 7: Applications of Integration

Section 1: Integration Techniques, Lhôpitals Rule, and Improper Integrals

Section 2: Integration Techniques, Lhôpitals Rule, and Improper Integrals

Section 3: Integration Techniques, Lhôpitals Rule, and Improper Integrals

Section 4: Integration Techniques, Lhôpitals Rule, and Improper Integrals

Section 5: Integration Techniques, Lhôpitals Rule, and Improper Integrals

Section 6: Integration Techniques, Lhôpitals Rule, and Improper Integrals

Section 7: Integration Techniques, Lhôpitals Rule, and Improper Integrals

Section 8: Integration Techniques, Lhôpitals Rule, and Improper Integrals

Section 1: Infinite Series

Section 2: Infinite Series

Section 3: Infinite Series

Section 4: Infinite Series