Question 1

Use the discriminant to classify the graph. ​   ​

Accepted Answer

A) The graph is a cone. 
B) The graph is a parabola. 
C) The graph is a ellipse or circle. 
D) The graph is a hyperbola. 
E) The graph is a line. 
A) The graph is a cone. 
B) The graph is a parabola. 
C) The graph is a ellipse or circle. 
D) The graph is a hyperbola. 
E) The graph is a line.

Question 2

Eliminate the parameter and write the corresponding rectangular equation whose graph represents the curve. ​     ​

Accepted Answer

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

Question 3

Find the standard form of the equation of the ellipse with vertices   and eccentricity   .

Accepted Answer

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

Question 4

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. ​
Vertical axis and passes through the point (6,8)
​

Accepted Answer

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

Question 5

Find the standard form of the equation of the ellipse with the given characteristics and center at the origin. ​
Focies: (±7,0); major axis of length 16
​

Accepted Answer

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

Question 6

You and a friend live 4 miles apart (on the same "east-west" street) and are talking on the phone.You hear a clap of thunder from lightning in a storm, and 16 seconds later your friend hears the thunder.Find an equation that gives the possible places where the lightning could have occurred.(Assume that the coordinate system is measured in feet and that sound travels at 1100 feet per second.)
​

Accepted Answer

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

Question 7

Select the graph of the equation. ​   ​

Accepted Answer

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

Question 8

Find the standard form of the equation of the ellipse with the given characteristics. ​
Vertices: (6,1), (6,17), minor axis of length 3
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Accepted Answer

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

Question 9

Find the standard form of the equation of the hyperbola with the given characteristics. foci:   asymptotes:

Accepted Answer

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

Question 10

Select the graph of the equation. ​   ​

Accepted Answer

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

Question 11

Identify the conic. ​   ​

Accepted Answer

A) Circle 
B) Ellipse 
C) Parabola 
D) Hyperbola 
E) Line 
A) Circle 
B) Ellipse 
C) Parabola 
D) Hyperbola 
E) Line

Question 12

Find the standard form of the equation of the hyperbola with the given characteristics. vertices: (3, 3), (3, 7)
Foci: (3, 1), (3, 9)
​

Accepted Answer

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

Question 13

Convert the rectangular equation to polar form.Assume r > 1. ​   ​

Accepted Answer

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

Question 14

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 15

Give the coordinates of the circle's center and it radius.
​   ​
Enter your answer using the coordinate notation: (a, b), and r = ....separated with a comma.

Accepted Answer

The answer of Give the coordinates of the circle's center...

Question 16

Select the correct graph of the polar equation.Find an interval for   for which the graph is traced only once. ​   ​

Accepted Answer

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

Question 17

Give the coordinates of the circle's center and its radius. ​   ​

Accepted Answer

A) (-6, 5); r = 4 
B) (6, -5); r = 2 
C) (6, -5); r = 4 
D) (-6, 5); r = 2 
E) none of these 
A) (-6, 5); r = 4 
B) (6, -5); r = 2 
C) (6, -5); r = 4 
D) (-6, 5); r = 2 
E) none of these

Question 18

Find the graph of the following ellipse. ​   ​

Accepted Answer

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

Question 19

Find the center and vertices of the hyperbola and select its graph, using asymptotes as sketching aids. ​   ​

Accepted Answer

A) Centre: (0,0) Vertices: (0,-5)   
B) Centre: (0,0) Vertices: (±5,0)   
C) Centre: (0,0) Vertices: (0,±5)   
D) Centre: (0,0) Vertices: (0,5)   
E) Centre: (0,0) Vertices: (5,0)   
A) Centre: (0,0) Vertices: (0,-5)   
B) Centre: (0,0) Vertices: (±5,0)   
C) Centre: (0,0) Vertices: (0,±5)   
D) Centre: (0,0) Vertices: (0,5)   
E) Centre: (0,0) Vertices: (5,0)

Question 20

The   -coordinate system has been rotated   degrees from the   -coordinate system.The coordinates of a point in the   -coordinate system are given.Find the coordinates of the point in the rotated coordinate system. ​   ,   ​

Accepted Answer

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

Use the discriminant to classify the graph.

Eliminate the parameter and write the corresponding rectangular equation whose graph represents the curve.

Find the standard form of the equation of the ellipse with vertices and eccentricity .

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. Vertical axis and passes through the point (6,8)

Find the standard form of the equation of the ellipse with the given characteristics and center at the origin. Focies: (±7,0); major axis of length 16

Select the graph of the equation.

Find the standard form of the equation of the ellipse with the given characteristics. Vertices: (6,1), (6,17), minor axis of length 3

Find the standard form of the equation of the hyperbola with the given characteristics. foci: asymptotes:

Select the graph of the equation.

Identify the conic.

Find the standard form of the equation of the hyperbola with the given characteristics. vertices: (3, 3), (3, 7) Foci: (3, 1), (3, 9)

Convert the rectangular equation to polar form.Assume r > 1.

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 coordinates of the circle's center and it radius. Enter your answer using the coordinate notation: (a, b), and r = ....separated with a comma.

Select the correct graph of the polar equation.Find an interval for for which the graph is traced only once.

Give the coordinates of the circle's center and its radius.

Find the graph of the following ellipse.

Find the center and vertices of the hyperbola and select its graph, using asymptotes as sketching aids.

The -coordinate system has been rotated degrees from the -coordinate system.The coordinates of a point in the -coordinate system are given.Find the coordinates of the point in the rotated coordinate system. ,

Trigonometry

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Exam 6: Topics-In-Analytic-Geometry

Use the discriminant to classify the graph. ​ ​

Eliminate the parameter and write the corresponding rectangular equation whose graph represents the curve. ​ ​

Find the standard form of the equation of the ellipse with vertices and eccentricity .

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. ​ Vertical axis and passes through the point (6,8) ​

Find the standard form of the equation of the ellipse with the given characteristics and center at the origin. ​ Focies: (±7,0); major axis of length 16 ​

Select the graph of the equation. ​ ​

Find the standard form of the equation of the ellipse with the given characteristics. ​ Vertices: (6,1), (6,17), minor axis of length 3 ​

Find the standard form of the equation of the hyperbola with the given characteristics. foci: asymptotes:

Select the graph of the equation. ​ ​

Identify the conic. ​ ​

Find the standard form of the equation of the hyperbola with the given characteristics. vertices: (3, 3), (3, 7) Foci: (3, 1), (3, 9) ​

Convert the rectangular equation to polar form.Assume r > 1. ​ ​

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 coordinates of the circle's center and it radius. ​ ​ Enter your answer using the coordinate notation: (a, b), and r = ....separated with a comma.

Select the correct graph of the polar equation.Find an interval for for which the graph is traced only once. ​ ​

Give the coordinates of the circle's center and its radius. ​ ​

Find the graph of the following ellipse. ​ ​

Find the center and vertices of the hyperbola and select its graph, using asymptotes as sketching aids. ​ ​

The -coordinate system has been rotated degrees from the -coordinate system.The coordinates of a point in the -coordinate system are given.Find the coordinates of the point in the rotated coordinate system. ​ , ​

Trigonometry

Analytic-Trigonometry

Additional-Topics-In-Trigonometry

Complex-Numbers

Exponential-And-Logarithmic-Functions

Prerequisites

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Use the discriminant to classify the graph.

Eliminate the parameter and write the corresponding rectangular equation whose graph represents the curve.

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. Vertical axis and passes through the point (6,8)

Find the standard form of the equation of the ellipse with the given characteristics and center at the origin. Focies: (±7,0); major axis of length 16

Select the graph of the equation.

Find the standard form of the equation of the ellipse with the given characteristics. Vertices: (6,1), (6,17), minor axis of length 3

Select the graph of the equation.

Identify the conic.

Find the standard form of the equation of the hyperbola with the given characteristics. vertices: (3, 3), (3, 7) Foci: (3, 1), (3, 9)

Convert the rectangular equation to polar form.Assume r > 1.

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 coordinates of the circle's center and it radius. Enter your answer using the coordinate notation: (a, b), and r = ....separated with a comma.

Select the correct graph of the polar equation.Find an interval for for which the graph is traced only once.

Give the coordinates of the circle's center and its radius.

Find the graph of the following ellipse.

Find the center and vertices of the hyperbola and select its graph, using asymptotes as sketching aids.

The -coordinate system has been rotated degrees from the -coordinate system.The coordinates of a point in the -coordinate system are given.Find the coordinates of the point in the rotated coordinate system. ,