Question 1

Find the standard form of the equation of the ellipse with the following characteristics. ​
Foci:   , major axis of length: 18
​

Accepted Answer

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

Question 2

Find the angle   (in radians and degrees) between the lines.Round your answer to four decimal places for radians and round your answer to one decimal places for degree.   ​

Accepted Answer

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

Question 3

Give the standard form of the equation of the parabola with the given characteristics. focus: (-3, 13) directrix:

Accepted Answer

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D)    
E)    
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B)    
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D)    
E)

Question 4

Consider the polar equation: ​   ​
Identify the conic without graphing the equation.
​

Accepted Answer

A)    , the conic is a parabola. 
B)    , the conic is a circle. 
C)    , the conic is a hyperbola. 
D)    , the conic is an ellipse. 
E) None of the above 
A)    , the conic is a parabola. 
B)    , the conic is a circle. 
C)    , the conic is a hyperbola. 
D)    , the conic is an ellipse. 
E) None of the above

Question 5

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. Focus:

Accepted Answer

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

Question 6

The equations of a parabola and a tangent line to the parabola are given.Select the correct graph of both equations in the same viewing window. ​
Parabola:   Tangent Line:   ​

Accepted Answer

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

Question 7

Find a set of parametric equations for the rectangular equation. ​     ​

Accepted Answer

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D)    
E)    
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D)    
E)

Question 8

The receiver in a parabolic satellite dish is 4.5 feet from the vertex and is located at the focus (see figure).Write an equation for a cross section of the reflector.(Assume that the dish is directed upward and the vertex is at the origin.) ​     ​

Accepted Answer

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

Question 9

Find the standard form of the equation of the ellipse with the following characteristics. ​
Foci:   , major axis of length: 16
​

Accepted Answer

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

Question 10

A moving conveyor is built so that it rises 7 meter for each 9 meters of horizontal travel.Select a diagram that gives a visual representation of the problem. ​

Accepted Answer

A) ​   a = 7m, b = 9m 
B) ​   a = 7m, b = 9m 
C) ​   a = 7m, b = 9m 
D) ​   a = 7m, b = 9m 
E) ​   a = 7m, b = 9m 
A) ​   a = 7m, b = 9m 
B) ​   a = 7m, b = 9m 
C) ​   a = 7m, b = 9m 
D) ​   a = 7m, b = 9m 
E) ​   a = 7m, b = 9m

Question 11

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points.
​   ​

Accepted Answer

A) Symmetric with respect to   , polar axis, pole Circle with radius  
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B) Symmetric with respect to   , polar axis, pole Circle with radius  
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C) Symmetric with respect to   , polar axis, pole Circle with radius  
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D) Symmetric with respect to   , polar axis, pole Circle with radius  
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E) Symmetric with respect to   , polar axis, pole Circle with radius  
​   
A) Symmetric with respect to   , polar axis, pole Circle with radius  
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B) Symmetric with respect to   , polar axis, pole Circle with radius  
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C) Symmetric with respect to   , polar axis, pole Circle with radius  
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D) Symmetric with respect to   , polar axis, pole Circle with radius  
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E) Symmetric with respect to   , polar axis, pole Circle with radius  
​

Question 12

Use the Quadratic Formula to solve for   . ​   ​

Accepted Answer

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

Question 13

Find the distance between the point and the line.Round your answer to four decimal places.   ​

Accepted Answer

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

Question 14

Select the correct equation of the following graph. ​   ​

Accepted Answer

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

Question 15

Consider a line with slope m and y-intercept (0,2).Write the distance d between the origin and the line as a function of m. ​

Accepted Answer

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

Question 16

Sketch the graph of the ellipse, using the latera recta. ​   ​

Accepted Answer

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

Question 17

Find the standard form of the equation of the ellipse with the given characteristics and center at the origin. ​
Vertical major axis passes through the points   .
​

Accepted Answer

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

Question 18

Convert the polar equation to rectangular form. ​   ​

Accepted Answer

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

Question 19

Find an equation of the ellipse with vertices   and eccentricity   . ​

Accepted Answer

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

Question 20

Find a set of parametric equations for the rectangular equation. ​   ​

Accepted Answer

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

Find the standard form of the equation of the ellipse with the following characteristics. Foci: , major axis of length: 18

Find the angle (in radians and degrees) between the lines.Round your answer to four decimal places for radians and round your answer to one decimal places for degree.

Give the standard form of the equation of the parabola with the given characteristics. focus: (-3, 13) directrix:

Consider the polar equation: Identify the conic without graphing the equation.

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. Focus:

The equations of a parabola and a tangent line to the parabola are given.Select the correct graph of both equations in the same viewing window. Parabola: Tangent Line:

Find a set of parametric equations for the rectangular equation.

The receiver in a parabolic satellite dish is 4.5 feet from the vertex and is located at the focus (see figure).Write an equation for a cross section of the reflector.(Assume that the dish is directed upward and the vertex is at the origin.)

Find the standard form of the equation of the ellipse with the following characteristics. Foci: , major axis of length: 16

A moving conveyor is built so that it rises 7 meter for each 9 meters of horizontal travel.Select a diagram that gives a visual representation of the problem.

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points.

Use the Quadratic Formula to solve for .

Find the distance between the point and the line.Round your answer to four decimal places.

Select the correct equation of the following graph.

Consider a line with slope m and y-intercept (0,2).Write the distance d between the origin and the line as a function of m.

Sketch the graph of the ellipse, using the latera recta.

Find the standard form of the equation of the ellipse with the given characteristics and center at the origin. Vertical major axis passes through the points .

Convert the polar equation to rectangular form.

Find an equation of the ellipse with vertices and eccentricity .

Find a set of parametric equations for the rectangular equation.

Trigonometry

Analytic-Trigonometry

Additional-Topics-In-Trigonometry

Complex-Numbers

Exponential-And-Logarithmic-Functions

Prerequisites

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Exam 6: Topics-In-Analytic-Geometry

Find the standard form of the equation of the ellipse with the following characteristics. ​ Foci: , major axis of length: 18 ​

Find the angle (in radians and degrees) between the lines.Round your answer to four decimal places for radians and round your answer to one decimal places for degree. ​

Give the standard form of the equation of the parabola with the given characteristics. focus: (-3, 13) directrix:

Consider the polar equation: ​ ​ Identify the conic without graphing the equation. ​

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. Focus:

The equations of a parabola and a tangent line to the parabola are given.Select the correct graph of both equations in the same viewing window. ​ Parabola: Tangent Line: ​

Find a set of parametric equations for the rectangular equation. ​ ​

The receiver in a parabolic satellite dish is 4.5 feet from the vertex and is located at the focus (see figure).Write an equation for a cross section of the reflector.(Assume that the dish is directed upward and the vertex is at the origin.) ​ ​

Find the standard form of the equation of the ellipse with the following characteristics. ​ Foci: , major axis of length: 16 ​

A moving conveyor is built so that it rises 7 meter for each 9 meters of horizontal travel.Select a diagram that gives a visual representation of the problem. ​

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points. ​ ​

Use the Quadratic Formula to solve for . ​ ​

Find the distance between the point and the line.Round your answer to four decimal places. ​

Select the correct equation of the following graph. ​ ​

Consider a line with slope m and y-intercept (0,2).Write the distance d between the origin and the line as a function of m. ​

Sketch the graph of the ellipse, using the latera recta. ​ ​

Find the standard form of the equation of the ellipse with the given characteristics and center at the origin. ​ Vertical major axis passes through the points . ​

Convert the polar equation to rectangular form. ​ ​

Find an equation of the ellipse with vertices and eccentricity . ​

Find a set of parametric equations for the rectangular equation. ​ ​

Trigonometry

Analytic-Trigonometry

Additional-Topics-In-Trigonometry

Complex-Numbers

Exponential-And-Logarithmic-Functions

Prerequisites

Filters

Find the standard form of the equation of the ellipse with the following characteristics. Foci: , major axis of length: 18

Find the angle (in radians and degrees) between the lines.Round your answer to four decimal places for radians and round your answer to one decimal places for degree.

Consider the polar equation: Identify the conic without graphing the equation.

The equations of a parabola and a tangent line to the parabola are given.Select the correct graph of both equations in the same viewing window. Parabola: Tangent Line:

Find a set of parametric equations for the rectangular equation.

The receiver in a parabolic satellite dish is 4.5 feet from the vertex and is located at the focus (see figure).Write an equation for a cross section of the reflector.(Assume that the dish is directed upward and the vertex is at the origin.)

Find the standard form of the equation of the ellipse with the following characteristics. Foci: , major axis of length: 16

A moving conveyor is built so that it rises 7 meter for each 9 meters of horizontal travel.Select a diagram that gives a visual representation of the problem.

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points.

Use the Quadratic Formula to solve for .

Find the distance between the point and the line.Round your answer to four decimal places.

Select the correct equation of the following graph.

Consider a line with slope m and y-intercept (0,2).Write the distance d between the origin and the line as a function of m.

Sketch the graph of the ellipse, using the latera recta.

Find the standard form of the equation of the ellipse with the given characteristics and center at the origin. Vertical major axis passes through the points .

Convert the polar equation to rectangular form.

Find an equation of the ellipse with vertices and eccentricity .

Find a set of parametric equations for the rectangular equation.