Question 1

Match the equation with its graph. ​   ​

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Question 2

Find the area of the surface generated by revolving the curve about the given axis.   (i) x-axis; (ii) y-axis

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Question 3

Convert the polar equation to rectangular form.

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Question 4

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

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Question 5

Find the eccentricity of the polar equation   .

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Question 6

Find the corresponding rectangular coordinates for the point   . Round your answer to three decimal places.

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Question 7

Find the area of the surface formed by revolving about the polar axis the following curve over the given interval.

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Question 8

Find the area of one petal of   .

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Question 9

Find the length of the curve over the given interval.

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Question 10

Identify the graph for the polar equation   .

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Question 11

Find   .

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Question 12

Find the area of the interior of   .

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Question 13

Classify the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola.

Accepted Answer

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

Question 14

Identify the conic for the polar equation   when   .

Accepted Answer

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

Question 15

Find the area of the surface generated by revolving the curve about the given axis.   (i) x-axis; (ii) y-axis

Accepted Answer

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

Question 16

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.
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B)  eccentricity:  
Distance from pole to directrix:  
The graph is a hyperbola.
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C)  eccentricity:  
Distance from pole to directrix:  
The graph is a hyperbola.
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D)  eccentricity:  
Distance from pole to directrix:  
The graph is an ellipse.
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E)  eccentricity:  
Distance from pole to directrix:  
The graph is an ellipse.
​   
A)  eccentricity:  
Distance from pole to directrix:  
The graph is an ellipse.
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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 17

Find a set of parametric equations for the rectangular equation   that satisfies the condition   at the point   .

Accepted Answer

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Question 18

Use the result, "the set of parametric equations for the ellipse is   " to find a set of parametric equations for the ellipse with vertices   and   and with foci at   and   . ​

Accepted Answer

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Question 19

Find the area of inside   and outside   by sketching the graph of the equations using the graphing utility. ​

Accepted Answer

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Question 20

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

Accepted Answer

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

Match the equation with its graph.

Find the area of the surface generated by revolving the curve about the given axis. (i) x-axis; (ii) y-axis

Convert the polar equation to rectangular form.

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

Find the eccentricity of the polar equation .

Find the corresponding rectangular coordinates for the point . Round your answer to three decimal places.

Find the area of the surface formed by revolving about the polar axis the following curve over the given interval.

Find the area of one petal of .

Find the length of the curve over the given interval.

Identify the graph for the polar equation .

Find .

Find the area of the interior of .

Classify the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola.

Identify the conic for the polar equation when .

Find the area of the surface generated by revolving the curve about the given axis. (i) x-axis; (ii) y-axis

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 set of parametric equations for the rectangular equation that satisfies the condition at the point .

Use the result, "the set of parametric equations for the ellipse is " to find a set of parametric equations for the ellipse with vertices and and with foci at and .

Find the area of inside and outside by sketching the graph of the equations using the graphing utility.

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

Preparation for Calculus

Limits and Their Properties

Differentiation

Applications of Differentiation

Integration

Differential Equations

Applications of Integration

Integration Techniques and Improper Integrals

Infinite Series

Vectors and the Geometry of Space

Vector-Valued Functions

Functions of Several Variables

Multiple Integration

Vector Anal

Filters

Exam 10: Conics, Parametric Equations, and Polar Coordinates

Match the equation with its graph. ​ ​

Find the area of the surface generated by revolving the curve about the given axis. (i) x-axis; (ii) y-axis

Convert the polar equation to rectangular form.

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

Find the eccentricity of the polar equation .

Find the corresponding rectangular coordinates for the point . Round your answer to three decimal places.

Find the area of the surface formed by revolving about the polar axis the following curve over the given interval.

Find the area of one petal of .

Find the length of the curve over the given interval.

Identify the graph for the polar equation .

Find .

Find the area of the interior of .

Classify the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola.

Identify the conic for the polar equation when .

Find the area of the surface generated by revolving the curve about the given axis. (i) x-axis; (ii) y-axis

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 set of parametric equations for the rectangular equation that satisfies the condition at the point .

Use the result, "the set of parametric equations for the ellipse is " to find a set of parametric equations for the ellipse with vertices and and with foci at and . ​

Find the area of inside and outside by sketching the graph of the equations using the graphing utility. ​

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

Preparation for Calculus

Limits and Their Properties

Differentiation

Applications of Differentiation

Integration

Differential Equations

Applications of Integration

Integration Techniques and Improper Integrals

Infinite Series

Vectors and the Geometry of Space

Vector-Valued Functions

Functions of Several Variables

Multiple Integration

Vector Anal

Filters

Match the equation with its graph.

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.

Use the result, "the set of parametric equations for the ellipse is " to find a set of parametric equations for the ellipse with vertices and and with foci at and .

Find the area of inside and outside by sketching the graph of the equations using the graphing utility.