Question 1

Sketch the parametric curve and eliminate the parameter to find the Cartesian equation of the curve.

Accepted Answer

The answer of Sketch the parametric curve and eliminate the...

Question 2

Find the area bounded by the curve   and the line y = 2.5.

Accepted Answer

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

Question 3

Find the polar equation for the curve represented by the given Cartesian equation.

Accepted Answer

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

Question 4

Find an equation of the hyperbola centered at the origin that satisfies the given condition. Vertices: (± 4, 0), asymptotes: y = ±   x

Accepted Answer

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

Question 5

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 6

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

Accepted Answer

The answer of Find the vertices, foci, and asymptotes of...

Question 7

Describe the motion of a particle with position   as t varies in the given interval   .

Accepted Answer

A) Moves once counterclockwise along the ellipse   starting and ending at   . 
B) Moves once counterclockwise along the circle   starting and ending at   . 
C) Moves once clockwise along the ellipse   starting and ending at   . 
D) Moves once counterclockwise along the ellipse   starting and ending at   . 
E) Moves once clockwise along the circle   starting and ending at   . 
A) Moves once counterclockwise along the ellipse   starting and ending at   . 
B) Moves once counterclockwise along the circle   starting and ending at   . 
C) Moves once clockwise along the ellipse   starting and ending at   . 
D) Moves once counterclockwise along the ellipse   starting and ending at   . 
E) Moves once clockwise along the circle   starting and ending at   .

Question 8

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

The answer of Consider the polar equation   .
(a)...

Question 9

Find the length of the polar curve.

Accepted Answer

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

Question 10

Use a graph to estimate the values of   for which the curves   and   intersect. Round your answer to two decimal places.

Accepted Answer

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

Question 11

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 12

Find the exact area of the surface obtained by rotating the given curve about the x-axis.

Accepted Answer

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

Question 13

Find an equation of the ellipse that satisfies the given conditions. Foci: (0, ± 1), vertices (0, ± 6)

Accepted Answer

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

Question 14

The orbit of Hale-Bopp comet, discovered in 1995, is an ellipse with eccentricity   and one focus at the Sun. The length of its major axis is   AU. [An astronomical unit (AU) is the mean distance between Earth and the Sun, about 93 million miles.] Find the maximum distance from the comet to the Sun. (The perihelion distance from a planet to the Sun is   and the aphelion distance is   .) Find the answer in AU and round to the nearest hundredth.

Accepted Answer

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

Question 15

Match the equation with the correct graph.

Accepted Answer

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

Question 16

Find the point(s) of intersection of the curves   and   .

Accepted Answer

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

Question 17

A cow is tied to a silo with radius   by a rope just long enough to reach the opposite side of the silo. Find the area available for grazing by the cow. Round the answer to the nearest hundredth.

Accepted Answer

The answer of A cow is tied to a silo...

Question 18

Find   .

Accepted Answer

The answer of Find   .  ...

Question 19

Find the area of the region that lies inside both curves.

Accepted Answer

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

Question 20

Eliminate the parameter to find a Cartesian equation of the curve.

Accepted Answer

The answer of Eliminate the parameter to find a Cartesian...

Sketch the parametric curve and eliminate the parameter to find the Cartesian equation of the curve.

Find the area bounded by the curve and the line y = 2.5.

Find the polar equation for the curve represented by the given Cartesian equation.

Find an equation of the hyperbola centered at the origin that satisfies the given condition. Vertices: (± 4, 0), asymptotes: y = ± x

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.

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

Describe the motion of a particle with position as t varies in the given interval .

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 the length of the polar curve.

Use a graph to estimate the values of for which the curves and intersect. Round your answer to two decimal places.

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

Find the exact area of the surface obtained by rotating the given curve about the x-axis.

Find an equation of the ellipse that satisfies the given conditions. Foci: (0, ± 1), vertices (0, ± 6)

Match the equation with the correct graph.

Find the point(s) of intersection of the curves and .

A cow is tied to a silo with radius by a rope just long enough to reach the opposite side of the silo. Find the area available for grazing by the cow. Round the answer to the nearest hundredth.

Find .

Find the area of the region that lies inside both curves.

Eliminate the parameter to find a Cartesian equation of the 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

Sketch the parametric curve and eliminate the parameter to find the Cartesian equation of the curve.

Find the area bounded by the curve and the line y = 2.5.

Find the polar equation for the curve represented by the given Cartesian equation.

Find an equation of the hyperbola centered at the origin that satisfies the given condition. Vertices: (± 4, 0), asymptotes: y = ± x

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.

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

Describe the motion of a particle with position as t varies in the given interval .

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 the length of the polar curve.

Use a graph to estimate the values of for which the curves and intersect. Round your answer to two decimal places.

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

Find the exact area of the surface obtained by rotating the given curve about the x-axis.

Find an equation of the ellipse that satisfies the given conditions. Foci: (0, ± 1), vertices (0, ± 6)

Match the equation with the correct graph.

Find the point(s) of intersection of the curves and .

A cow is tied to a silo with radius by a rope just long enough to reach the opposite side of the silo. Find the area available for grazing by the cow. Round the answer to the nearest hundredth.

Find .

Find the area of the region that lies inside both curves.

Eliminate the parameter to find a Cartesian equation of the 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