Question 1

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. focus: (0, -2)

Accepted Answer

A) y2 = -8x 
B) x2 = -8y 
C) x2 = -2y 
D) y2 = -2x 
E) x2 = 2y 
A) y2 = -8x 
B) x2 = -8y 
C) x2 = -2y 
D) y2 = -2x 
E) x2 = 2y

Question 2

Find the standard form of the equation of the ellipse with the given characteristics. ​
Foci:   , endpoints of the major axis:   ​

Accepted Answer

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

Question 3

Find any points of intersection of the graphs algebraically. ​   ​

Accepted Answer

A) The points of intersection are   and   . 
B) The points of intersection are   and   . 
C) The points of intersection are   and   . 
D) The points of intersection are   and   . 
E) The points of intersection are   and   . 
A) The points of intersection are   and   . 
B) The points of intersection are   and   . 
C) The points of intersection are   and   . 
D) The points of intersection are   and   . 
E) The points of intersection are   and   .

Question 4

Find the inclination   (in radians and degrees) of the line.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

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 6

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

Accepted Answer

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

Question 7

Find the standard form of the equation of the hyperbola with the given characteristics and center at the origin. ​
Vertices:   ; asymptotes:   ​

Accepted Answer

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

Question 8

A point in rectangular coordinates is given.Convert the point to polar coordinates, r > 0. ​   ​

Accepted Answer

A) ​​Polar coordinates:   ​ 
B) Polar coordinates:   
C) Polar coordinates:   
D) Polar coordinates:   
E) Polar coordinates:   
A) ​​Polar coordinates:   ​ 
B) Polar coordinates:   
C) Polar coordinates:   
D) Polar coordinates:   
E) Polar coordinates:

Question 9

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)

Question 10

A solar oven uses a parabolic reflector to focus the sun's rays at a point 5 inches from the vertex of the reflector (see figure).   L = 5 inches ​
Write an equation for a cross section of the oven's reflector with its focus on the positive y axis and its vertex at the origin.

Accepted Answer

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

Question 11

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 12

Find the vertex, focus, and directrix of the parabola. ​   ​

Accepted Answer

A) Vertex: (0,0); Focus:   ; Directrix:   
B) Vertex:(0,0) ; Focus:   ; Directrix:   
C) Vertex: (0,0); Focus:   ; Directrix:   
D) Vertex: (0,0); Focus:   ; Directrix:   
E) Vertex: (0,0); Focus:   ; Directrix:   
A) Vertex: (0,0); Focus:   ; Directrix:   
B) Vertex:(0,0) ; Focus:   ; Directrix:   
C) Vertex: (0,0); Focus:   ; Directrix:   
D) Vertex: (0,0); Focus:   ; Directrix:   
E) Vertex: (0,0); Focus:   ; Directrix:

Question 13

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

Question 14

Find the standard form of the equation of the parabola with the given characteristics. ​
Vertex:   ; focus:   ​

Accepted Answer

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

Question 15

Find the equation of the circle graphed below. ​   ​

Accepted Answer

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

Question 16

Find the vertex, focus, and directrix of the parabola. ​   ​

Accepted Answer

A) Vertex: (0,0); Focus:   ; Directrix:   
B) Vertex: (0,0); Focus:   ; Directrix:   
C) Vertex: (0,0); Focus:   ; Directrix:   
D) Vertex: (0,0); Focus:   ; Directrix:   
E) Vertex: (0,0); Focus:   ; Directrix:   
A) Vertex: (0,0); Focus:   ; Directrix:   
B) Vertex: (0,0); Focus:   ; Directrix:   
C) Vertex: (0,0); Focus:   ; Directrix:   
D) Vertex: (0,0); Focus:   ; Directrix:   
E) Vertex: (0,0); Focus:   ; Directrix:

Question 17

Select the correct graph of the polar equation.Describe your viewing window. ​   ​

Accepted Answer

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

Question 18

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 19

Find the vertex and focus of the parabola.

Accepted Answer

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

Question 20

Select the correct graph of the polar equation.Describe your viewing window. ​   ​

Accepted Answer

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

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. focus: (0, -2)

Find the standard form of the equation of the ellipse with the given characteristics. Foci: , endpoints of the major axis:

Find any points of intersection of the graphs algebraically.

Find the inclination (in radians and degrees) of the line.Round your answer to four decimal places for radians and round your answer to one decimal places for degree.

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

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 and center at the origin. Vertices: ; asymptotes:

A point in rectangular coordinates is given.Convert the point to polar coordinates, r > 0.

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. ,

A solar oven uses a parabolic reflector to focus the sun's rays at a point 5 inches from the vertex of the reflector (see figure). L = 5 inches Write an equation for a cross section of the oven's reflector with its focus on the positive y axis and its vertex at the origin.

Identify the conic and select its correct graph.

Find the vertex, focus, and directrix of the parabola.

Find the center, vertices and foci of the hyperbola.

Find the standard form of the equation of the parabola with the given characteristics. Vertex: ; focus:

Find the equation of the circle graphed below.

Find the vertex, focus, and directrix of the parabola.

Select the correct graph of the polar equation.Describe your viewing window.

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

Find the vertex and focus of the parabola.

Select the correct graph of the polar equation.Describe your viewing window.

Trigonometry

Analytic-Trigonometry

Additional-Topics-In-Trigonometry

Complex-Numbers

Exponential-And-Logarithmic-Functions

Prerequisites

Filters

Exam 6: Topics-In-Analytic-Geometry

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. focus: (0, -2)

Find the standard form of the equation of the ellipse with the given characteristics. ​ Foci: , endpoints of the major axis: ​

Find any points of intersection of the graphs algebraically. ​ ​

Find the inclination (in radians and degrees) of the line.Round your answer to four decimal places for radians and round your answer to one decimal places for degree. ​ ​

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

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 and center at the origin. ​ Vertices: ; asymptotes: ​

A point in rectangular coordinates is given.Convert the point to polar coordinates, r > 0. ​ ​

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. ​ , ​

A solar oven uses a parabolic reflector to focus the sun's rays at a point 5 inches from the vertex of the reflector (see figure). L = 5 inches ​ Write an equation for a cross section of the oven's reflector with its focus on the positive y axis and its vertex at the origin.

Identify the conic and select its correct graph. ​ ​

Find the vertex, focus, and directrix of the parabola. ​ ​

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

Find the standard form of the equation of the parabola with the given characteristics. ​ Vertex: ; focus: ​

Find the equation of the circle graphed below. ​ ​

Find the vertex, focus, and directrix of the parabola. ​ ​

Select the correct graph of the polar equation.Describe your viewing window. ​ ​

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

Find the vertex and focus of the parabola.

Select the correct graph of the polar equation.Describe your viewing window. ​ ​

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 given characteristics. Foci: , endpoints of the major axis:

Find any points of intersection of the graphs algebraically.

Find the inclination (in radians and degrees) of the line.Round your answer to four decimal places for radians and round your answer to one decimal places for degree.

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

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 and center at the origin. Vertices: ; asymptotes:

A point in rectangular coordinates is given.Convert the point to polar coordinates, r > 0.

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. ,

A solar oven uses a parabolic reflector to focus the sun's rays at a point 5 inches from the vertex of the reflector (see figure). L = 5 inches Write an equation for a cross section of the oven's reflector with its focus on the positive y axis and its vertex at the origin.

Identify the conic and select its correct graph.

Find the vertex, focus, and directrix of the parabola.

Find the center, vertices and foci of the hyperbola.

Find the standard form of the equation of the parabola with the given characteristics. Vertex: ; focus:

Find the equation of the circle graphed below.

Find the vertex, focus, and directrix of the parabola.

Select the correct graph of the polar equation.Describe your viewing window.

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

Select the correct graph of the polar equation.Describe your viewing window.