Question 1

Convert the rectangular equation to polar form.Assume a > 0, r > 1. ​   ​

Accepted Answer

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

Question 2

Find the center, vertices and foci of the hyperbola. ​   ​

Accepted Answer

A) Center: (0, 0) Vertices:  
Foci:   
B) Center:   Vertices:  
Foci:   
C) Center: (0, 0) Vertices:  
Foci:   
D) Center:   Vertices: ​  
Foci:   
E) Center:   Vertices:  
Foci:   
A) Center: (0, 0) Vertices:  
Foci:   
B) Center:   Vertices:  
Foci:   
C) Center: (0, 0) Vertices:  
Foci:   
D) Center:   Vertices: ​  
Foci:   
E) Center:   Vertices:  
Foci:

Question 3

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

Accepted Answer

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

Question 4

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 5

Select the curve represented by the parametric equations. ​   ​

Accepted Answer

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

Question 6

Find the standard form of the equation of the parabola with the given characteristic(s) and vertex at the origin. ​
Directrix: y = -1
​

Accepted Answer

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

Question 7

Identify the conic as a circle or an ellipse then find the center. ​   ​

Accepted Answer

A) Circle Center: (0,0) 
B) Ellipse Center: (0,0) 
C) Circle Center: (7,0) 
D) Ellipse Center: (0,7) 
E) ​Circle Center: (7,7) 
A) Circle Center: (0,0) 
B) Ellipse Center: (0,0) 
C) Circle Center: (7,0) 
D) Ellipse Center: (0,7) 
E) ​Circle Center: (7,7)

Question 8

Find the vertex and focus of the parabola from the given equation and select its graph. ​   ​

Accepted Answer

A) Vertex: (0,0) Focus: (0,-1.5)   ​ 
B) Vertex: (0,0) Focus: (-1.5,0)   
C) Vertex: (0,0) Focus: (0,1.5)   
D) Vertex: (0,0) Focus: (0,1.5)   
E) Vertex: (0,0) Focus: (0,-1.5)   
A) Vertex: (0,0) Focus: (0,-1.5)   ​ 
B) Vertex: (0,0) Focus: (-1.5,0)   
C) Vertex: (0,0) Focus: (0,1.5)   
D) Vertex: (0,0) Focus: (0,1.5)   
E) Vertex: (0,0) Focus: (0,-1.5)

Question 9

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

Accepted Answer

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

Question 10

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

Accepted Answer

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

Question 11

Identify the conic by writing the equation in standard form. ​   ​

Accepted Answer

A)    ; ellipse 
B)    ; circle 
C)    ; ellipse 
D)    ; ellipse 
E)    ; ellipse 
A)    ; ellipse 
B)    ; circle 
C)    ; ellipse 
D)    ; ellipse 
E)    ; ellipse

Question 12

Find the standard form of the equation of the ellipse with the given characteristics. ​
​vertices: (-1, -11), (-1, 7), minor axis of length 2
​

Accepted Answer

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

Question 13

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

A projectile is launched at a height of h feet above the ground at an angle of   with the horizontal.The initial velocity is   feet per second, and the path of the projectile is modeled by the parametric equations   . Select the correct graph of the path of a projectile launched from ground level at the value of   and   .
​   feet per second
​

Accepted Answer

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

Question 16

Identify the conic and select its correct graph. ​   ​

Accepted Answer

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

Question 17

Consider the equation   .Select the correct graph of the equation for   . ​

Accepted Answer

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

Question 18

Identify the conic by writing the equation in standard form. ​   ​

Accepted Answer

A) ​   ; ellipse 
B) ​   ; hyperbola 
C) ​   ; hyperbola 
D) ​   ; hyperbola 
E) ​   ; ellipse 
A) ​   ; ellipse 
B) ​   ; hyperbola 
C) ​   ; hyperbola 
D) ​   ; hyperbola 
E) ​   ; ellipse

Question 19

Find the standard form of the equation of the hyperbola with the given characteristics and center at the origin. ​
Vertices: (0,±5); focies: (0,±6)
​

Accepted Answer

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

Question 20

Any sound from one focus of an ellipse reflects off the ellipse directly back to the other focus.This property explains whispering galleries such as Statuary Hall in Washington, D.C.The whispering gallery shown in illustration has the shape of a semi-circle.Find the distance sound travels as it leaves focus F and returns to focus F'.Round your answer to one decimal place, if necessary. ​   ​

Accepted Answer

A) 16 meters 
B) 16.8 meters 
C) 33.5 meters 
D) 32 meters 
E) 31.2 meters 
A) 16 meters 
B) 16.8 meters 
C) 33.5 meters 
D) 32 meters 
E) 31.2 meters

Convert the rectangular equation to polar form.Assume a > 0, r > 1.

Find the center, vertices and foci of the hyperbola.

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

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.

Select the curve represented by the parametric equations.

Find the standard form of the equation of the parabola with the given characteristic(s) and vertex at the origin. Directrix: y = -1

Identify the conic as a circle or an ellipse then find the center.

Find the vertex and focus of the parabola from the given equation and select its graph.

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

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

Identify the conic by writing the equation in standard form.

Find the standard form of the equation of the ellipse with the given characteristics. vertices: (-1, -11), (-1, 7), minor axis of length 2

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

Identify the conic and select its correct graph.

Consider the equation .Select the correct graph of the equation for .

Identify the conic by writing the equation in standard form.

Find the standard form of the equation of the hyperbola with the given characteristics and center at the origin. Vertices: (0,±5); focies: (0,±6)

Trigonometry

Analytic-Trigonometry

Additional-Topics-In-Trigonometry

Complex-Numbers

Exponential-And-Logarithmic-Functions

Prerequisites

Filters

Exam 6: Topics-In-Analytic-Geometry

Convert the rectangular equation to polar form.Assume a > 0, r > 1. ​ ​

Find the center, vertices and foci of the hyperbola. ​ ​

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

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. ​ ​

Select the curve represented by the parametric equations. ​ ​

Find the standard form of the equation of the parabola with the given characteristic(s) and vertex at the origin. ​ Directrix: y = -1 ​

Identify the conic as a circle or an ellipse then find the center. ​ ​

Find the vertex and focus of the parabola from the given equation and select its graph. ​ ​

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

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

Identify the conic by writing the equation in standard form. ​ ​

Find the standard form of the equation of the ellipse with the given characteristics. ​ ​vertices: (-1, -11), (-1, 7), minor axis of length 2 ​

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

Identify the conic and select its correct graph. ​ ​

Consider the equation .Select the correct graph of the equation for . ​

Identify the conic by writing the equation in standard form. ​ ​

Find the standard form of the equation of the hyperbola with the given characteristics and center at the origin. ​ Vertices: (0,±5); focies: (0,±6) ​

Trigonometry

Analytic-Trigonometry

Additional-Topics-In-Trigonometry

Complex-Numbers

Exponential-And-Logarithmic-Functions

Prerequisites

Filters

Convert the rectangular equation to polar form.Assume a > 0, r > 1.

Find the center, vertices and foci of the hyperbola.

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

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.

Select the curve represented by the parametric equations.

Find the standard form of the equation of the parabola with the given characteristic(s) and vertex at the origin. Directrix: y = -1

Identify the conic as a circle or an ellipse then find the center.

Find the vertex and focus of the parabola from the given equation and select its graph.

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

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

Identify the conic by writing the equation in standard form.

Find the standard form of the equation of the ellipse with the given characteristics. vertices: (-1, -11), (-1, 7), minor axis of length 2

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

Identify the conic and select its correct graph.

Consider the equation .Select the correct graph of the equation for .

Identify the conic by writing the equation in standard form.

Find the standard form of the equation of the hyperbola with the given characteristics and center at the origin. Vertices: (0,±5); focies: (0,±6)