Question 1

Find the point(s) on the curve where the tangent is horizontal.

Accepted Answer

A)    
B)    
C)    
D)    
E) None of these 
A)    
B)    
C)    
D)    
E) None of these

Question 2

Select the curve by using the parametric equations to plot the points.

Accepted Answer

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

Question 3

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...

Question 4

Find the eccentricity of the conic.

Accepted Answer

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

Question 5

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 6

Write a polar equation in r and   of a hyperbola with the focus at the origin, with the eccentricity   and directrix   .

Accepted Answer

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

Question 7

The planet Mercury travels in an elliptical orbit with eccentricity   . Its minimum distance from the Sun is   km. If the perihelion distance from a planet to the Sun is   and the aphelion distance is   , find the maximum distance (in km) from Mercury to the Sun.

Accepted Answer

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

Question 8

Write a polar equation of the conic that has a focus at the origin, eccentricity   , and directrix   . Identify the conic.

Accepted Answer

A)    , ellipse 
B)    , hyperbola 
C)    , hyperbola 
D)    , ellipse 
A)    , ellipse 
B)    , hyperbola 
C)    , hyperbola 
D)    , ellipse

Question 9

Find the area that the curve encloses.

Accepted Answer

The answer of Find the area that the curve encloses....

Question 10

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)

Find the point(s) on the curve where the tangent is horizontal.

Select the curve by using the parametric equations to plot the points.

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

Find the eccentricity of the conic.

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

Write a polar equation in r and of a hyperbola with the focus at the origin, with the eccentricity and directrix .

The planet Mercury travels in an elliptical orbit with eccentricity . Its minimum distance from the Sun is km. If the perihelion distance from a planet to the Sun is and the aphelion distance is , find the maximum distance (in km) from Mercury to the Sun.

Write a polar equation of the conic that has a focus at the origin, eccentricity , and directrix . Identify the conic.

Find the area that the curve encloses.

Functions and Limits

Derivatives

Inverse Functions: Exponential, Logarithmic, and Inverse Trigonometric Functions

Applications of Differentiation

Integrals

Techniques of Integration

Applications of Integration

Series

Vectors and the Geometry of Space

Partial Derivatives

Multiple Integrals

Vector Calculus

Filters

Exam 9: Parametric Equations and Polar Coordinates

Find the point(s) on the curve where the tangent is horizontal.

Select the curve by using the parametric equations to plot the points.

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

Find the eccentricity of the conic.

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

Write a polar equation in r and of a hyperbola with the focus at the origin, with the eccentricity and directrix .

The planet Mercury travels in an elliptical orbit with eccentricity . Its minimum distance from the Sun is km. If the perihelion distance from a planet to the Sun is and the aphelion distance is , find the maximum distance (in km) from Mercury to the Sun.

Write a polar equation of the conic that has a focus at the origin, eccentricity , and directrix . Identify the conic.

Find the area that the curve encloses.

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

Functions and Limits

Derivatives

Inverse Functions: Exponential, Logarithmic, and Inverse Trigonometric Functions

Applications of Differentiation

Integrals

Techniques of Integration

Applications of Integration

Series

Vectors and the Geometry of Space

Partial Derivatives

Multiple Integrals

Vector Calculus

Filters