Question 1

The ellipse given by the equations    , has a minor axis of length ____ units.

Accepted Answer

The answer of The ellipse given by the equations ...

Question 2

Give a parameterization for the straight line segment joining the points (4,2) and (-4,-4).

Accepted Answer

The answer of Give a parameterization for the straight line...

Question 3

Describe the graph of the parametric equations   for t > 0.

Accepted Answer

A)  A circle of radius 6, centered at the origin and traced in the clockwise direction. 
B)  The right half of a circle of radius 6, centered at the origin, traced in the clockwise direction, and never quite reaching the point (0, 6). 
C)  The lower half of a circle of radius 6, centered at the origin, traced in the counterclockwise direction, and never quite reaching the point (6, 0). 
D)  The upper half of a circle of radius 6, centered at the origin, traced in the clockwise direction, and never quite reaching the point (6, 0). 
A)  A circle of radius 6, centered at the origin and traced in the clockwise direction. 
B)  The right half of a circle of radius 6, centered at the origin, traced in the clockwise direction, and never quite reaching the point (0, 6). 
C)  The lower half of a circle of radius 6, centered at the origin, traced in the counterclockwise direction, and never quite reaching the point (6, 0). 
D)  The upper half of a circle of radius 6, centered at the origin, traced in the clockwise direction, and never quite reaching the point (6, 0).

Question 4

An elliptical whispering gallery has a major axis of 28 feet an a minor axis of 22 feet. Where should two speakers position themselves so as to most easily hear each other?

Accepted Answer

A)  5.34 feet in from the ends of the minor axis 
B)  8.66 feet in from the ends of the minor axis 
C)  5.34 feet in from the ends of the major axis 
D)  8.66 feet in from the ends of the major axis 
A)  5.34 feet in from the ends of the minor axis 
B)  8.66 feet in from the ends of the minor axis 
C)  5.34 feet in from the ends of the major axis 
D)  8.66 feet in from the ends of the major axis

Question 5

Let   be the equation of the ellipse shown below. Assuming that the x- and y-scales are equal, which of the following is true?

Accepted Answer

A)  k < h < 0 < a < b 
B)  h < k < 0 < b < a 
C)  k < h < 0 < b < a 
D)  h < k < 0 < a < b 
A)  k < h < 0 < a < b 
B)  h < k < 0 < b < a 
C)  k < h < 0 < b < a 
D)  h < k < 0 < a < b

Question 6

Let an ellipse be parameterized by the equations   .
a) What is the center?
b) What is the length of the major axis?
c) What is the length of the minor axis?
d) Find an implicit equation of the curve.

Accepted Answer

a)(-5,2)
b

Question 7

Write    as   for some a and b.

Accepted Answer

The answer of Write    as  ...

Question 8

Describe the graph of the curve   
.

Accepted Answer

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

Question 9

What is the radius of the circle    ?

Accepted Answer

The answer of What is the radius of the circle...

Question 10

A search light uses a 6 ft wide parabolic mirror that is 3 ft deep. If the lamp is positioned 0.250 ft above the center of the mirror, how wide is the beam in the sky?

Accepted Answer

The answer of A search light uses a 6 ft...

Question 11

As   , what does
  approach?

Accepted Answer

A)  0 
B)    
C)  -    
A)  0 
B)    
C)  -

Question 12

What curve is parameterized by the functions    and   ? Give an implicit or explicit equation for the curve.

Accepted Answer

The answer of What curve is parameterized by the functions...

Question 13

The equation of the parabola centered at the origin with focal point (0, -2) is 
   
.

Accepted Answer

The answer of The equation of the parabola centered at...

Question 14

What is the focus of the parabola 
   ?

Accepted Answer

The answer of What is the focus of the parabola...

Question 15

Give a parameterization for the upper half circle of radius 3 centered at (7,-4), and starting at (10,-4)

Accepted Answer

The answer of Give a parameterization for the upper half...

Question 16

Find a parameterization of the curve    so that the curve is traversed in a counter-clockwise direction starting at

Accepted Answer

The answer of Find a parameterization of the curve ...

Question 17

Write    as   for some a and b.

Accepted Answer

The answer of Write    as  ...

Question 18

Find the center of the ellipse and the lengths of the major and minor axes:

Accepted Answer

The answer of Find the center of the ellipse and...

Question 19

If the circle    is converted to the parametric equations   , then h = _____, k = _____, and r = _____.

Accepted Answer

The answer of If the circle    is...

Question 20

Let y = t be one part of a parametric equation. Which of the following formulas for x as a function of t on   completes the parameterization of the graph of a straight line from (0, 0) to (1, 1), and then continuing from (1, 1) in a straight line to (0, 2)?

Accepted Answer

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

The ellipse given by the equations , has a minor axis of length ____ units.

Give a parameterization for the straight line segment joining the points (4,2) and (-4,-4).

Describe the graph of the parametric equations for t > 0.

An elliptical whispering gallery has a major axis of 28 feet an a minor axis of 22 feet. Where should two speakers position themselves so as to most easily hear each other?

Let be the equation of the ellipse shown below. Assuming that the x- and y-scales are equal, which of the following is true?

Let an ellipse be parameterized by the equations . a) What is the center? b) What is the length of the major axis? c) What is the length of the minor axis? d) Find an implicit equation of the curve.

Write as for some a and b.

Describe the graph of the curve .

What is the radius of the circle ?

A search light uses a 6 ft wide parabolic mirror that is 3 ft deep. If the lamp is positioned 0.250 ft above the center of the mirror, how wide is the beam in the sky?

As , what does approach?

What curve is parameterized by the functions and ? Give an implicit or explicit equation for the curve.

The equation of the parabola centered at the origin with focal point (0, -2) is .

What is the focus of the parabola ?

Give a parameterization for the upper half circle of radius 3 centered at (7,-4), and starting at (10,-4)

Find a parameterization of the curve so that the curve is traversed in a counter-clockwise direction starting at

Write as for some a and b.

Find the center of the ellipse and the lengths of the major and minor axes:

If the circle is converted to the parametric equations , then h = ___, k = _, and r = ___.

Let y = t be one part of a parametric equation. Which of the following formulas for x as a function of t on completes the parameterization of the graph of a straight line from (0, 0) to (1, 1), and then continuing from (1, 1) in a straight line to (0, 2)?

Linear Functions and Change

Functions

Quadratic Functions

Exponential Functions

Logarithmic Functions

Transformations of Functions and Their Graphs

Trigonometry in Circles and Triangles

Trigonometric Functions

Trigonometric Identities and Their Applications

Compositions, Inverses, and Combinations of Functions

Polynomial and Rational Functions

Vectors and Matrices

Sequences and Series

Filters

Exam 14: Parametric Equations and Conic Sections

The ellipse given by the equations , has a minor axis of length ____ units.

Give a parameterization for the straight line segment joining the points (4,2) and (-4,-4).

Describe the graph of the parametric equations for t > 0.

An elliptical whispering gallery has a major axis of 28 feet an a minor axis of 22 feet. Where should two speakers position themselves so as to most easily hear each other?

Let be the equation of the ellipse shown below. Assuming that the x- and y-scales are equal, which of the following is true?

Let an ellipse be parameterized by the equations . a) What is the center? b) What is the length of the major axis? c) What is the length of the minor axis? d) Find an implicit equation of the curve.

Write as for some a and b.

Describe the graph of the curve .

What is the radius of the circle ?

A search light uses a 6 ft wide parabolic mirror that is 3 ft deep. If the lamp is positioned 0.250 ft above the center of the mirror, how wide is the beam in the sky?

As , what does approach?

What curve is parameterized by the functions and ? Give an implicit or explicit equation for the curve.

The equation of the parabola centered at the origin with focal point (0, -2) is .

What is the focus of the parabola ?

Give a parameterization for the upper half circle of radius 3 centered at (7,-4), and starting at (10,-4)

Find a parameterization of the curve so that the curve is traversed in a counter-clockwise direction starting at

Write as for some a and b.

Find the center of the ellipse and the lengths of the major and minor axes:

If the circle is converted to the parametric equations , then h = _____, k = _____, and r = _____.

Let y = t be one part of a parametric equation. Which of the following formulas for x as a function of t on completes the parameterization of the graph of a straight line from (0, 0) to (1, 1), and then continuing from (1, 1) in a straight line to (0, 2)?

Linear Functions and Change

Functions

Quadratic Functions

Exponential Functions

Logarithmic Functions

Transformations of Functions and Their Graphs

Trigonometry in Circles and Triangles

Trigonometric Functions

Trigonometric Identities and Their Applications

Compositions, Inverses, and Combinations of Functions

Polynomial and Rational Functions

Vectors and Matrices

Sequences and Series

Filters

If the circle is converted to the parametric equations , then h = ___, k = _, and r = ___.