Question 1

Find a polar equation for the conic section with focus   and the given directrix and eccentricity. Directrix

Accepted Answer

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

Question 2

Sketch the plane curve defined by the given parametric equations.

Accepted Answer

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

Question 3

Find a polar equation corresponding to the given rectangular equation.

Accepted Answer

A)    
B)    
C)  r = 6 
D)    
A)    
B)    
C)  r = 6 
D)

Question 4

Find the area of the indicated region. One leaf of

Accepted Answer

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

Question 5

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

Accepted Answer

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

Question 6

Find all points of intersection of the two curves.

Accepted Answer

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

Question 7

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

Accepted Answer

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

Question 8

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 x = 2, e = 1

Accepted Answer

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

Question 9

Find an equation for the indicated conic section. Ellipse with foci (3, -2), (-13, -2) and vertices (12, -2), (-22, -2)

Accepted Answer

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

Question 10

Find an equation for the conic section with the given properties. All points such that the sum of the distances to the points
(-4, -2) and (-4, 14) equals 20

Accepted Answer

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

Question 11

Find parametric equations describing the given curve.
The line segment from   to

Accepted Answer

Answers ma

Question 12

Find a corresponding x-y equation.

Accepted Answer

A)    
B)    
C)  x = 3 
D)  x2 + y2 = 3 
A)    
B)    
C)  x = 3 
D)  x2 + y2 = 3

Question 13

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

Accepted Answer

A)  (1, 0) 
B)  (0, 2), (2, 0) 
C)  (2, 0), (0, 2), (-2, 0), (0, -2) 
D)  (1, 1), (-1, 1) 
A)  (1, 0) 
B)  (0, 2), (2, 0) 
C)  (2, 0), (0, 2), (-2, 0), (0, -2) 
D)  (1, 1), (-1, 1)

Question 14

Use a CAS or graphing calculator to sketch the plane curve defined by the given parametric equations. Use a window size of [-5, 5] by [-5, 5].

Accepted Answer

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

Question 15

Plot the given polar point.

Accepted Answer

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

Question 16

Find all polar coordinate representations of the given rectangular point.

Accepted Answer

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

Question 17

Which of the following sets of parametric equations is equivalent to   ?

Accepted Answer

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

Question 18

Find the slope of the tangent line to the polar curve at the given point.

Accepted Answer

A)    
B)    
C)    
D)  1 
A)    
B)    
C)    
D)  1

Question 19

Find the area of the indicated region. Round to the nearest ten-thousandth. Inside of both r = 1 and

Accepted Answer

A)  1.3460 
B)  3.1416 
C)  1.2310 
D)  0.6730 
A)  1.3460 
B)  3.1416 
C)  1.2310 
D)  0.6730

Question 20

The orbits of the planets can be modeled easily by assuming i). that the sun is a perfect sphere and ii). that each planet is influenced only by the gravitational field of the sun (that is, each planet is unperturbed by gravitational forces from other planets, distant stars, etc.). According to Newton's (classical) theory of gravity, these assumptions result in elliptical planetary orbits with the sun at one focus. That is, the orbit can be described by the polar equation   . However, according to Einstein's (relativistic) theory of gravitation, the orbits are more accurately described by   , where   is a constant such that   . Describe how the inclusion of the factor   affects the orbit. That is, compare the classical orbit to the relativistic orbit. How do they differ? Draw figures that summarize the differences in the classical and relativistic orbits.

Accepted Answer

The period of the relativistic orbit is

Find a polar equation for the conic section with focus and the given directrix and eccentricity. Directrix

Sketch the plane curve defined by the given parametric equations.

Find a polar equation corresponding to the given rectangular equation.

Find the area of the indicated region. One leaf of

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

Find all points of intersection of the two curves.

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

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 x = 2, e = 1

Find an equation for the indicated conic section. Ellipse with foci (3, -2), (-13, -2) and vertices (12, -2), (-22, -2)

Find an equation for the conic section with the given properties. All points such that the sum of the distances to the points (-4, -2) and (-4, 14) equals 20

Find parametric equations describing the given curve. The line segment from to

Find a corresponding x-y equation.

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

Use a CAS or graphing calculator to sketch the plane curve defined by the given parametric equations. Use a window size of [-5, 5] by [-5, 5].

Plot the given polar point.

Find all polar coordinate representations of the given rectangular point.

Which of the following sets of parametric equations is equivalent to ?

Find the slope of the tangent line to the polar curve at the given point.

Find the area of the indicated region. Round to the nearest ten-thousandth. Inside of both r = 1 and

Preliminaries

Limits and Continuity

Differentiation

Applications of the Derivative

Integration

Applications of the Definite Integral

Exponentials, Logarithms and Other Transcendental Functions

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 11: Parametric Equations and Polar Coordinates

Find a polar equation for the conic section with focus and the given directrix and eccentricity. Directrix

Sketch the plane curve defined by the given parametric equations.

Find a polar equation corresponding to the given rectangular equation.

Find the area of the indicated region. One leaf of

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

Find all points of intersection of the two curves.

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

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 x = 2, e = 1

Find an equation for the indicated conic section. Ellipse with foci (3, -2), (-13, -2) and vertices (12, -2), (-22, -2)

Find an equation for the conic section with the given properties. All points such that the sum of the distances to the points (-4, -2) and (-4, 14) equals 20

Find parametric equations describing the given curve. The line segment from to

Find a corresponding x-y equation.

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

Use a CAS or graphing calculator to sketch the plane curve defined by the given parametric equations. Use a window size of [-5, 5] by [-5, 5].

Plot the given polar point.

Find all polar coordinate representations of the given rectangular point.

Which of the following sets of parametric equations is equivalent to ?

Find the slope of the tangent line to the polar curve at the given point.

Find the area of the indicated region. Round to the nearest ten-thousandth. Inside of both r = 1 and

Preliminaries

Limits and Continuity

Differentiation

Applications of the Derivative

Integration

Applications of the Definite Integral

Exponentials, Logarithms and Other Transcendental Functions

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