Question 1

Find all polar coordinate representations of the given rectangular point.

Accepted Answer

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

Question 2

Find the arc length of the curve. Approximate numerically, if needed.

Accepted Answer

A)  12 
B)  6 
C)  12$\pi$ 
D)  2$\pi$ 
A)  12 
B)  6 
C)  12$\pi$ 
D)  2$\pi$

Question 3

Plot the given polar point.

Accepted Answer

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

Question 4

Find an equation for the conic section with the given properties. All points such that the sum of the distances to the points
(7, 0) and (7, -10) equals 26

Accepted Answer

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

Question 5

Find parametric equations describing the given curve.
The circle of radius 4 centered at   , drawn counterclockwise

Accepted Answer

Answers ma

Question 6

Find all points at which |r| is a maximum.

Accepted Answer

A)  (1, 0) 
B)  (0, 8), (8, 0) 
C)  (8, 0), (0, 8), (-8, 0), (0, -8) 
D)  (1, 1), (-1, 1) 
A)  (1, 0) 
B)  (0, 8), (8, 0) 
C)  (8, 0), (0, 8), (-8, 0), (0, -8) 
D)  (1, 1), (-1, 1)

Question 7

Use a graphing utility to graph the conic section with focus (0, 0) and the given directrix and eccentricity. Use a window size of [-3, 3] by [-3, 3]. Directrix y = -1, e = 3

Accepted Answer

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

Question 8

Find rectangular coordinates for the given polar point.

Accepted Answer

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

Question 9

Identify all values of   where r = 0.

Accepted Answer

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

Question 10

For the given parametric equations, find a corresponding x-y equation for the curve.

Accepted Answer

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

Question 11

Find parametric equations for the path of a projectile launched from height   ft with initial speed   ft/s at angle   from the horizontal.

Accepted Answer

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

Question 12

Find parametric equations describing the given curve.
The portion of the parabola   from   to

Accepted Answer

Answers ma

Question 13

Find a corresponding x-y equation. r = 4

Accepted Answer

A)    
B)  x2 + y2 = 16 
C)    
D)  x2 + y2 = 4 
A)    
B)  x2 + y2 = 16 
C)    
D)  x2 + y2 = 4

Question 14

Starting with the parametric arc length formula   and the equations relating polar and cartesian coordinates, show that the arc length of the polar curve   on the interval [a, b] is given by

Accepted Answer

Let the pa

Question 15

Sketch the graph of the polar equation. (Find a corresponding x-y equation if it helps.)

Accepted Answer

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

Question 16

Compute the surface area of the surface obtained by revolving the given curve about the indicated axis.

Accepted Answer

A)  237.13 
B)  470.92 
C)  840.14 
D)  34.55 
A)  237.13 
B)  470.92 
C)  840.14 
D)  34.55

Question 17

Identify a range of values of   that produces one copy of the graph.

Accepted Answer

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

Question 18

Find all points of intersection of the two curves.

Accepted Answer

A)    
B)    
C)    
D)  The curves have no points of intersection. 
A)    
B)    
C)    
D)  The curves have no points of intersection.

Question 19

Find a polar equation for the conic section with focus (0, 0) and the given directrix and eccentricity. Directrix y = -3, e = 4

Accepted Answer

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

Question 20

Find all points at which the two curves intersect. Round to the nearest ten-thousandth.

Accepted Answer

A)  (0, 0), (0.2338, 0.2025), (1.7457, 1.5118) 
B)  (0, 0) 
C)  (0.2338, -0.2025), (1.7457, -1.5118) 
D)  (0, 0), (0, 1), (0, -1) 
A)  (0, 0), (0.2338, 0.2025), (1.7457, 1.5118) 
B)  (0, 0) 
C)  (0.2338, -0.2025), (1.7457, -1.5118) 
D)  (0, 0), (0, 1), (0, -1)

Find all polar coordinate representations of the given rectangular point.

Find the arc length of the curve. Approximate numerically, if needed.

Plot the given polar point.

Find an equation for the conic section with the given properties. All points such that the sum of the distances to the points (7, 0) and (7, -10) equals 26

Find parametric equations describing the given curve. The circle of radius 4 centered at , drawn counterclockwise

Find all points at which |r| is a maximum.

Use a graphing utility to graph the conic section with focus (0, 0) and the given directrix and eccentricity. Use a window size of [-3, 3] by [-3, 3]. Directrix y = -1, e = 3

Find rectangular coordinates for the given polar point.

Identify all values of where r = 0.

For the given parametric equations, find a corresponding x-y equation for the curve.

Find parametric equations for the path of a projectile launched from height ft with initial speed ft/s at angle from the horizontal.

Find parametric equations describing the given curve. The portion of the parabola from to

Find a corresponding x-y equation. r = 4

Starting with the parametric arc length formula and the equations relating polar and cartesian coordinates, show that the arc length of the polar curve on the interval [a, b] is given by

Sketch the graph of the polar equation. (Find a corresponding x-y equation if it helps.)

Compute the surface area of the surface obtained by revolving the given curve about the indicated axis.

Identify a range of values of that produces one copy of the graph.

Find all points of intersection of the two curves.

Find a polar equation for the conic section with focus (0, 0) and the given directrix and eccentricity. Directrix y = -3, e = 4

Find all points at which the two curves intersect. Round to the nearest ten-thousandth.

Preliminaries

Limits and Continuity

Differentiation

Applications of the Derivative

Integration

Applications of the Definite Integral

Integration Techniques

First-Order Differential Equations

Infinite Series

Vectors and the Geometry of Space

Vector-Valued Functions

Functions of Several Variables and Partial Differentiation

Multiple Integrals

Vector Calculus

Second Order Differential Equations

Filters

Exam 10: Parametric Equations and Polar Coordinates

Find all polar coordinate representations of the given rectangular point.

Find the arc length of the curve. Approximate numerically, if needed.

Plot the given polar point.

Find an equation for the conic section with the given properties. All points such that the sum of the distances to the points (7, 0) and (7, -10) equals 26

Find parametric equations describing the given curve. The circle of radius 4 centered at , drawn counterclockwise

Find all points at which |r| is a maximum.

Use a graphing utility to graph the conic section with focus (0, 0) and the given directrix and eccentricity. Use a window size of [-3, 3] by [-3, 3]. Directrix y = -1, e = 3

Find rectangular coordinates for the given polar point.

Identify all values of where r = 0.

For the given parametric equations, find a corresponding x-y equation for the curve.

Find parametric equations for the path of a projectile launched from height ft with initial speed ft/s at angle from the horizontal.

Find parametric equations describing the given curve. The portion of the parabola from to

Find a corresponding x-y equation. r = 4

Starting with the parametric arc length formula and the equations relating polar and cartesian coordinates, show that the arc length of the polar curve on the interval [a, b] is given by

Sketch the graph of the polar equation. (Find a corresponding x-y equation if it helps.)

Compute the surface area of the surface obtained by revolving the given curve about the indicated axis.

Identify a range of values of that produces one copy of the graph.

Find all points of intersection of the two curves.

Find a polar equation for the conic section with focus (0, 0) and the given directrix and eccentricity. Directrix y = -3, e = 4

Find all points at which the two curves intersect. Round to the nearest ten-thousandth.

Preliminaries

Limits and Continuity

Differentiation

Applications of the Derivative

Integration

Applications of the Definite Integral

Integration Techniques

First-Order Differential Equations

Infinite Series

Vectors and the Geometry of Space

Vector-Valued Functions

Functions of Several Variables and Partial Differentiation

Multiple Integrals

Vector Calculus

Second Order Differential Equations

Filters