Question 1

Consider the polar equation   .
(a) Find the eccentricity and an equation of the directrix of the conic.
(b) Identify the conic.
(c) Sketch the curve.

Accepted Answer

a.  
b. ellipse
c.

Question 2

Find an equation of the hyperbola with vertices   and asymptotes   .

Accepted Answer

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

Question 3

Find the surface area generated by rotating the lemniscate   about the line   .

Accepted Answer

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

Question 4

Find an equation for the conic that satisfies the given conditions. parabola, vertex (0, 0), focus (0, -   )

Accepted Answer

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

Question 5

Find an equation of the parabola with focus   and directrix   .

Accepted Answer

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

Question 6

Suppose a planet is discovered that revolves around its sun in an elliptical orbit with the sun at one focus. Its perihelion distance (minimum distance from the planet to the sun) is approximately 1.3   km, and its aphelion distance (maximum distance from the planet to the sun) is approximately 6.9   km. Approximate the eccentricity of the planet's orbit. Round to three decimal places.

Accepted Answer

A) 0.683 
B) 1.464 
C) 5.308 
D) 0.188 
A) 0.683 
B) 1.464 
C) 5.308 
D) 0.188

Question 7

Write a polar equation in r and $\theta$ of an ellipse with the focus at the origin, with the eccentricity   and directrix   .

Accepted Answer

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

Question 8

Find a Cartesian equation for the curve described by the given polar equation.

Accepted Answer

The answer of Find a Cartesian equation for the curve...

Question 9

Find the area of the region that is bounded by the given curve and lies in the specified sector.

Accepted Answer

The answer of Find the area of the region that...

Question 10

The graph of the following curve is given. Find the area that it encloses.

Accepted Answer

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

Question 11

Set up an integral that represents the length of the curve. Then use your calculator to find the length correct to four decimal places.

Accepted Answer

The answer of Set up an integral that represents the...

Question 12

The point in a lunar orbit nearest the surface of the moon is called perilune and the point farthest from the surface is called apolune. The Apollo 11 spacecraft was placed in an elliptical lunar orbit with perilune altitude   km and apolune altitude   km (above the moon). Find an equation of this ellipse if the radius of the moon is   km and the center of the moon is at one focus.

Accepted Answer

The answer of The point in a lunar orbit nearest...

Question 13

Using the arc length formula, set up, but do not evaluate, an integral equal to the total arc length of the ellipse.

Accepted Answer

The answer of Using the arc length formula, set up,...

Question 14

Find the eccentricity of the conic.

Accepted Answer

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

Question 15

Find the area enclosed by the curve   .

Accepted Answer

The answer of Find the area enclosed by the curve...

Question 16

The curve   cross itself at some point   . Find the equations of both tangent lines at that point.

Accepted Answer

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

Question 17

Find the area of the region that lies inside the first curve and outside the second curve.

Accepted Answer

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

Question 18

Write a polar equation in r and $\theta$of an ellipse with the focus at the origin, with the eccentricity   and vertex at   .

Accepted Answer

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

Question 19

Find an equation of the tangent to the curve at the point corresponding to the given value of the parameter.

Accepted Answer

The answer of Find an equation of the tangent to...

Question 20

Set up, but do not evaluate, an integral that represents the length of the parametric curve.

Accepted Answer

The answer of Set up, but do not evaluate, an...

Consider the polar equation . (a) Find the eccentricity and an equation of the directrix of the conic. (b) Identify the conic. (c) Sketch the curve.

Find an equation of the hyperbola with vertices and asymptotes .

Find the surface area generated by rotating the lemniscate about the line .

Find an equation for the conic that satisfies the given conditions. parabola, vertex (0, 0), focus (0, - )

Find an equation of the parabola with focus and directrix .

Find a Cartesian equation for the curve described by the given polar equation.

Find the area of the region that is bounded by the given curve and lies in the specified sector.

The graph of the following curve is given. Find the area that it encloses.

Set up an integral that represents the length of the curve. Then use your calculator to find the length correct to four decimal places.

Using the arc length formula, set up, but do not evaluate, an integral equal to the total arc length of the ellipse.

Find the eccentricity of the conic.

Find the area enclosed by the curve .

The curve cross itself at some point . Find the equations of both tangent lines at that point.

Find the area of the region that lies inside the first curve and outside the second curve.

Find an equation of the tangent to the curve at the point corresponding to the given value of the parameter.

Set up, but do not evaluate, an integral that represents the length of the parametric curve.

Functions and Limits

Derivatives

Applications of Differentiation

Integrals

Applications of Integration

Inverse Functions

Techniques of Integration

Further Applications of Integration

Differential Equations

Infinite Sequences and Series

Vectors and the Geometry of Space

Vector Functions

Partial Derivatives

Multiple Integrals

Vector Calculus

Second-Order Differential Equations

Final Exam

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Exam 10: Parametric Equations and Polar Coordinates

Consider the polar equation . (a) Find the eccentricity and an equation of the directrix of the conic. (b) Identify the conic. (c) Sketch the curve.

Find an equation of the hyperbola with vertices and asymptotes .

Find the surface area generated by rotating the lemniscate about the line .

Find an equation for the conic that satisfies the given conditions. parabola, vertex (0, 0), focus (0, - )

Find an equation of the parabola with focus and directrix .

Write a polar equation in r and θ\thetaθ of an ellipse with the focus at the origin, with the eccentricity and directrix .

Find a Cartesian equation for the curve described by the given polar equation.

Find the area of the region that is bounded by the given curve and lies in the specified sector.

The graph of the following curve is given. Find the area that it encloses.

Set up an integral that represents the length of the curve. Then use your calculator to find the length correct to four decimal places.

Using the arc length formula, set up, but do not evaluate, an integral equal to the total arc length of the ellipse.

Find the eccentricity of the conic.

Find the area enclosed by the curve .

The curve cross itself at some point . Find the equations of both tangent lines at that point.

Find the area of the region that lies inside the first curve and outside the second curve.

Write a polar equation in r and θ\thetaθ of an ellipse with the focus at the origin, with the eccentricity and vertex at .

Find an equation of the tangent to the curve at the point corresponding to the given value of the parameter.

Set up, but do not evaluate, an integral that represents the length of the parametric curve.

Functions and Limits

Derivatives

Applications of Differentiation

Integrals

Applications of Integration

Inverse Functions

Techniques of Integration

Further Applications of Integration

Differential Equations

Infinite Sequences and Series

Vectors and the Geometry of Space

Vector Functions

Partial Derivatives

Multiple Integrals

Vector Calculus

Second-Order Differential Equations

Final Exam

Filters