Question 1

Find the standard form of the equation of the hyperbola with the given characteristics and center at the origin. ​
Vertices: (±3,0); passes through the point ​   ​

Accepted Answer

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

Question 2

Identify the conic and select its correct graph. ​   ​

Accepted Answer

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

Question 3

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

Question 4

Select the graph of degenerate conic. ​   ​

Accepted Answer

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

Question 5

Find the vertex and directrix of the parabola.

Accepted Answer

A) vertex:   directrix: y=1 
B) vertex:   directrix: y=12 
C) vertex:   directrix: y=6 
D) vertex:   directrix: y=-1 
E) vertex:   directrix: y=-7 
A) vertex:   directrix: y=1 
B) vertex:   directrix: y=12 
C) vertex:   directrix: y=6 
D) vertex:   directrix: y=-1 
E) vertex:   directrix: y=-7

Question 6

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 7

Identify the conic as a circle or an ellipse. ​   ​

Accepted Answer

A) Circle 
B) Ellipse 
A) Circle 
B) Ellipse

Question 8

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

Accepted Answer

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

Question 9

Find the standard form of the equation of the ellipse with the given characteristics and center at the origin. ​   ​

Accepted Answer

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

Question 10

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

Accepted Answer

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

Question 11

Find the center and vertices of the ellipse. ​   ​

Accepted Answer

A) center: (-8, 9), vertices: (-10, 9), (-6, 9) 
B) center: (9, -8), vertices: (7, -8), (11, -8) 
C) center: (-9, 8), vertices: (-10, 8), (-8, 8) 
D) center: (-9, 8), vertices: (-11, 8), (-7, 8) 
E) center: (9, -8), vertices: (8, -8), (10, -8) 
A) center: (-8, 9), vertices: (-10, 9), (-6, 9) 
B) center: (9, -8), vertices: (7, -8), (11, -8) 
C) center: (-9, 8), vertices: (-10, 8), (-8, 8) 
D) center: (-9, 8), vertices: (-11, 8), (-7, 8) 
E) center: (9, -8), vertices: (8, -8), (10, -8)

Question 12

Select correct graph to graph rotated conic. ​   ​

Accepted Answer

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

Question 13

Select the graph of the conic. ​   ​

Accepted Answer

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

Question 14

Write the equation of the hyperbola with vertices (4, 0), (-4, 0) and focus (5, 0).

Accepted Answer

The answer of Write the equation of the hyperbola with...

Question 15

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 16

Find the standard form of the equation of the ellipse with the given characteristics. ​
Center:   , a = 5c, foci:   , where a - thr semimajor axis, b - semiminor axis and   .

Accepted Answer

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

Question 17

Use the following results the polar equation of the hyperbolla   is   to write the polar form of the equation of the conic   . ​

Accepted Answer

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

Question 18

Select the correct graph of the following equations of the hyperbola and find the center of the hyperbola. ​   ​

Accepted Answer

A) Center: (2, - 3)   
B) Center: (0, 0)   
C) Center: (2, - 3)   
D) Center: (0, 0)   ​ 
E) Center: (2, - 3)   
A) Center: (2, - 3)   
B) Center: (0, 0)   
C) Center: (2, - 3)   
D) Center: (0, 0)   ​ 
E) Center: (2, - 3)

Question 19

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 20

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

Accepted Answer

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

Find the standard form of the equation of the hyperbola with the given characteristics and center at the origin. Vertices: (±3,0); passes through the point

Identify the conic and select its correct graph.

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

Select the graph of degenerate conic.

Find the vertex and directrix of the parabola.

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

Identify the conic as a circle or an ellipse.

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 and center at the origin.

Find the center, vertices and foci of the hyperbola.

Find the center and vertices of the ellipse.

Select correct graph to graph rotated conic.

Select the graph of the conic.

Write the equation of the hyperbola with vertices (4, 0), (-4, 0) and focus (5, 0).

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

Find the standard form of the equation of the ellipse with the given characteristics. Center: , a = 5c, foci: , where a - thr semimajor axis, b - semiminor axis and .

Use the following results the polar equation of the hyperbolla is to write the polar form of the equation of the conic .

Select the correct graph of the following equations of the hyperbola and find the center of the hyperbola.

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

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

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 hyperbola with the given characteristics and center at the origin. ​ Vertices: (±3,0); passes through the point ​ ​

Identify the conic and select its correct graph. ​ ​

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

Select the graph of degenerate conic. ​ ​

Find the vertex and directrix of the parabola.

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

Identify the conic as a circle or an ellipse. ​ ​

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 and center at the origin. ​ ​

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

Find the center and vertices of the ellipse. ​ ​

Select correct graph to graph rotated conic. ​ ​

Select the graph of the conic. ​ ​

Write the equation of the hyperbola with vertices (4, 0), (-4, 0) and focus (5, 0).

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

Find the standard form of the equation of the ellipse with the given characteristics. ​ Center: , a = 5c, foci: , where a - thr semimajor axis, b - semiminor axis and .

Use the following results the polar equation of the hyperbolla is to write the polar form of the equation of the conic . ​

Select the correct graph of the following equations of the hyperbola and find the center of the hyperbola. ​ ​

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

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

Trigonometry

Analytic-Trigonometry

Additional-Topics-In-Trigonometry

Complex-Numbers

Exponential-And-Logarithmic-Functions

Prerequisites

Filters

Find the standard form of the equation of the hyperbola with the given characteristics and center at the origin. Vertices: (±3,0); passes through the point

Identify the conic and select its correct graph.

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

Select the graph of degenerate conic.

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

Identify the conic as a circle or an ellipse.

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 and center at the origin.

Find the center, vertices and foci of the hyperbola.

Find the center and vertices of the ellipse.

Select correct graph to graph rotated conic.

Select the graph of the conic.

Find the standard form of the equation of the ellipse with the given characteristics. Center: , a = 5c, foci: , where a - thr semimajor axis, b - semiminor axis and .

Use the following results the polar equation of the hyperbolla is to write the polar form of the equation of the conic .

Select the correct graph of the following equations of the hyperbola and find the center of the hyperbola.

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

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