Question 1

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 2

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

Accepted Answer

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

Question 3

Find the vertices of the ellipse given by   . ​

Accepted Answer

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

Question 4

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

Accepted Answer

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

Question 5

Find   and   if possible, and find the slope and concavity (if possible) at the point corresponding to   .

Accepted Answer

A)    at   : slope 1 and concave up 
B)    at   : slope -1 and concave up 
C)    at   : slope -1 and concave down 
D)    at   : slope 1 and concave down 
E)    at   : slope of -1 and concave up 
A)    at   : slope 1 and concave up 
B)    at   : slope -1 and concave up 
C)    at   : slope -1 and concave down 
D)    at   : slope 1 and concave down 
E)    at   : slope of -1 and concave up

Question 6

The parametric equations for the path of a projectile launched at a height h feet above the ground, at an angle   with the horizontal and having an initial velocity of   feet per second is given by   and   . The center field fence in a ballpark is 10 feet high and 400 feet from home plate. The ball is hit 2 feet above the ground. It leaves the bat at an angle of   degrees with the horizontal at a speed of 95 miles per hour as shown in the figure. Find the minimum angle at which the ball must leave the bat in order for the hit to be a home run using the parametric equations   and   . Round your answer to one decimal place. ​   ​

Accepted Answer

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

Question 7

Find the center, foci, and vertices of the hyperbola.

Accepted Answer

A)  center:   ; vertices:   ,   ; foci:   ,   . 
B)  center:   ; vertices:   ,   ; foci:   ,   . 
C)  center:   ; vertices:   ,   ; foci:   ,   . 
D)  center:   ; vertices:   ,   ; foci:   ,   . 
E)  center:   ; vertices:   ,   ; foci:   ,   . 
A)  center:   ; vertices:   ,   ; foci:   ,   . 
B)  center:   ; vertices:   ,   ; foci:   ,   . 
C)  center:   ; vertices:   ,   ; foci:   ,   . 
D)  center:   ; vertices:   ,   ; foci:   ,   . 
E)  center:   ; vertices:   ,   ; foci:   ,   .

Question 8

Find the directrix of the parabola given by   .

Accepted Answer

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

Question 9

Find the center, foci, vertices, and eccentricity of the ellipse. ​   ​

Accepted Answer

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

Question 10

Find the foci of the ellipse given by   .

Accepted Answer

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

Question 11

Convert the rectangular equation   to polar form.

Accepted Answer

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

Question 12

Neptune moves in an elliptical orbit with the sun at one of the foci. The length of the half of the major axis is 4,502,899,800 kilometers, and the eccentricity is 0.0112. Find the maximum distance (aphelion) of Neptune from the sun. Round your answer to nearest kilometer. ​

Accepted Answer

A)  4,412,841,804 km 
B)  50,432,478 km 
C)  4,592,957,796 km 
D)  4,553,332,278 km 
E)  4,452,467,322 km 
A)  4,412,841,804 km 
B)  50,432,478 km 
C)  4,592,957,796 km 
D)  4,553,332,278 km 
E)  4,452,467,322 km

Question 13

Use the result, "the set of parametric equations for the line passing through   and   is   " to find a set of parametric equations for the line passing through   and   .

Accepted Answer

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

Question 14

Find the area of the surface generated by revolving the curve   about the x-axis on the interval   .

Accepted Answer

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

Question 15

Identify the graph for the polar equation   .

Accepted Answer

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

Question 16

Find the arc length of the curve on the given interval.

Accepted Answer

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

Question 17

Find all points of intersection of the graphs of the equations. ​   ​

Accepted Answer

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

Question 18

Determine the t intervals on which the curve   is concave downward or concave upward.

Accepted Answer

A)  concave downward:   ; concave upward:   
B)  concave downward:   ; concave upward:   
C)  concave downward:   ; concave upward:   
D)  concave downward:   ; concave upward:   
E)  concave downward:   ; concave upward:   
A)  concave downward:   ; concave upward:   
B)  concave downward:   ; concave upward:   
C)  concave downward:   ; concave upward:   
D)  concave downward:   ; concave upward:   
E)  concave downward:   ; concave upward:

Question 19

Find the points of intersection of the graphs of the equations.

Accepted Answer

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

Question 20

Find two sets of polar coordinates for the point   for   .

Accepted Answer

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

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

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

Find the vertices of the ellipse given by .

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

Find and if possible, and find the slope and concavity (if possible) at the point corresponding to .

Find the center, foci, and vertices of the hyperbola.

Find the directrix of the parabola given by .

Find the center, foci, vertices, and eccentricity of the ellipse.

Find the foci of the ellipse given by .

Convert the rectangular equation to polar form.

Neptune moves in an elliptical orbit with the sun at one of the foci. The length of the half of the major axis is 4,502,899,800 kilometers, and the eccentricity is 0.0112. Find the maximum distance (aphelion) of Neptune from the sun. Round your answer to nearest kilometer.

Use the result, "the set of parametric equations for the line passing through and is " to find a set of parametric equations for the line passing through and .

Find the area of the surface generated by revolving the curve about the x-axis on the interval .

Identify the graph for the polar equation .

Find the arc length of the curve on the given interval.

Find all points of intersection of the graphs of the equations.

Determine the t intervals on which the curve is concave downward or concave upward.

Find the points of intersection of the graphs of the equations.

Find two sets of polar coordinates for the point for .

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

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

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

Find the vertices of the ellipse given by . ​

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

Find and if possible, and find the slope and concavity (if possible) at the point corresponding to .

Find the center, foci, and vertices of the hyperbola.

Find the directrix of the parabola given by .

Find the center, foci, vertices, and eccentricity of the ellipse. ​ ​

Find the foci of the ellipse given by .

Convert the rectangular equation to polar form.

Neptune moves in an elliptical orbit with the sun at one of the foci. The length of the half of the major axis is 4,502,899,800 kilometers, and the eccentricity is 0.0112. Find the maximum distance (aphelion) of Neptune from the sun. Round your answer to nearest kilometer. ​

Use the result, "the set of parametric equations for the line passing through and is " to find a set of parametric equations for the line passing through and .

Find the area of the surface generated by revolving the curve about the x-axis on the interval .

Identify the graph for the polar equation .

Find the arc length of the curve on the given interval.

Find all points of intersection of the graphs of the equations. ​ ​

Determine the t intervals on which the curve is concave downward or concave upward.

Find the points of intersection of the graphs of the equations.

Find two sets of polar coordinates for the point for .

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

Find the vertices of the ellipse given by .

Find the center, foci, vertices, and eccentricity of the ellipse.

Neptune moves in an elliptical orbit with the sun at one of the foci. The length of the half of the major axis is 4,502,899,800 kilometers, and the eccentricity is 0.0112. Find the maximum distance (aphelion) of Neptune from the sun. Round your answer to nearest kilometer.

Find all points of intersection of the graphs of the equations.