Question 1

Select the graph of the following equation ​   ​

Accepted Answer

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

Question 2

Identify the conic and select its correct graph. ​   ​

Accepted Answer

A)    Hyperbola ​  
​
​ 
B)    Ellipse ​   
C)    Hyperbola ​   
D)    Ellipse ​  
​ 
E)    Hyperbola ​   
A)    Hyperbola ​  
​
​ 
B)    Ellipse ​   
C)    Hyperbola ​   
D)    Ellipse ​  
​ 
E)    Hyperbola ​   D

Question 3

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)    D

Question 4

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 5

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     ​   
B) Symmetric with respect to     ​   
C) Symmetric with respect to     ​   
D) Symmetric with respect to     ​   
E) Symmetric with respect to     ​   
A) Symmetric with respect to     ​   
B) Symmetric with respect to     ​   
C) Symmetric with respect to     ​   
D) Symmetric with respect to     ​   
E) Symmetric with respect to     ​

Question 6

Select the polar equation of graph. ​   ​

Accepted Answer

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

Question 7

A roof has a rise of 9 feet for every horizontal change of 11 feet (see figure).Find the inclination of the roof.Round your answers to one decimal place. ​   ​   ​

Accepted Answer

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

Question 8

Find the distance between the point and the line. ​   ​

Accepted Answer

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

Question 9

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 the polar axis,   , and the pole
Lemniscate
​   
B) Symmetric with respect to the polar axis,   , and the pole
Lemniscate
​   
C) Symmetric with respect to the polar axis,   , and the pole
Lemniscate
​   
D) Symmetric with respect to the polar axis,   , and the pole
Lemniscate
​   
E) Symmetric with respect to the polar axis,   , and the pole
Lemniscate
​   
A) Symmetric with respect to the polar axis,   , and the pole
Lemniscate
​   
B) Symmetric with respect to the polar axis,   , and the pole
Lemniscate
​   
C) Symmetric with respect to the polar axis,   , and the pole
Lemniscate
​   
D) Symmetric with respect to the polar axis,   , and the pole
Lemniscate
​   
E) Symmetric with respect to the polar axis,   , and the pole
Lemniscate
​

Question 10

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

Accepted Answer

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

Question 11

Convert the rectangular equation to polar form.Assume a > 0, r > 0. ​   ​

Accepted Answer

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

Question 12

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

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 standard form of the equation of the parabola and determine the coordinates of the focus.

Accepted Answer

A)    focus:   
B)    focus:   
C)    focus:   
D)    focus:   
E)    focus: (0, 4) 
A)    focus:   
B)    focus:   
C)    focus:   
D)    focus:   
E)    focus: (0, 4)

Question 15

Select the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola. ​   ​

Accepted Answer

A) Circle 
B) Parabola 
C) Hyperbola 
D) Ellipse 
E) None of the above 
A) Circle 
B) Parabola 
C) Hyperbola 
D) Ellipse 
E) None of the above

Question 16

Match the equation with its graph.

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. ​
Foci:   ; major axis of length 10.
​

Accepted Answer

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

Question 18

Find the standard form of the equation of the ellipse with the following characteristics. ​
Foci:   , major axis of length: 22
​
​

Accepted Answer

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

Question 19

Identify the conic and select its correct graph. ​   ​

Accepted Answer

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

Question 20

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. focus: (0, -1)

Accepted Answer

A) y2 = -4x 
B) x2 = -4y 
C) x2 = y 
D) y2 = -x 
E) x2 = -y 
A) y2 = -4x 
B) x2 = -4y 
C) x2 = y 
D) y2 = -x 
E) x2 = -y

Select the graph of the following equation

Identify the conic and select its correct graph.

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

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

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

Select the polar equation of graph.

A roof has a rise of 9 feet for every horizontal change of 11 feet (see figure).Find the inclination of the roof.Round your answers to one decimal place.

Find the distance between the point and the line.

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

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

Convert the rectangular equation to polar form.Assume a > 0, r > 0.

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

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

Find the standard form of the equation of the parabola and determine the coordinates of the focus.

Select the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola.

Match the equation with its graph.

Find the standard form of the equation of the ellipse with the given characteristics. Foci: ; major axis of length 10.

Find the standard form of the equation of the ellipse with the following characteristics. Foci: , major axis of length: 22

Identify the conic and select its correct graph.

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. focus: (0, -1)

Trigonometry

Analytic-Trigonometry

Additional-Topics-In-Trigonometry

Complex-Numbers

Exponential-And-Logarithmic-Functions

Prerequisites

Filters

Exam 6: Topics-In-Analytic-Geometry

Select the graph of the following equation ​ ​

Identify the conic and select its correct graph. ​ ​

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

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

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

Select the polar equation of graph. ​ ​

A roof has a rise of 9 feet for every horizontal change of 11 feet (see figure).Find the inclination of the roof.Round your answers to one decimal place. ​ ​ ​

Find the distance between the point and the line. ​ ​

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

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

Convert the rectangular equation to polar form.Assume a > 0, r > 0. ​ ​

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

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

Find the standard form of the equation of the parabola and determine the coordinates of the focus.

Select the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola. ​ ​

Match the equation with its graph.

Find the standard form of the equation of the ellipse with the given characteristics. ​ Foci: ; major axis of length 10. ​

Find the standard form of the equation of the ellipse with the following characteristics. ​ Foci: , major axis of length: 22 ​ ​

Identify the conic and select its correct graph. ​ ​

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. focus: (0, -1)

Trigonometry

Analytic-Trigonometry

Additional-Topics-In-Trigonometry

Complex-Numbers

Exponential-And-Logarithmic-Functions

Prerequisites

Filters

Select the graph of the following equation

Identify the conic and select its correct graph.

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

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

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

Select the polar equation of graph.

A roof has a rise of 9 feet for every horizontal change of 11 feet (see figure).Find the inclination of the roof.Round your answers to one decimal place.

Find the distance between the point and the line.

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

Convert the rectangular equation to polar form.Assume a > 0, r > 0.

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

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

Select the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola.

Find the standard form of the equation of the ellipse with the given characteristics. Foci: ; major axis of length 10.

Find the standard form of the equation of the ellipse with the following characteristics. Foci: , major axis of length: 22

Identify the conic and select its correct graph.