Question 1

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   ​   
B) Symmetric with respect to the polar axis   ​   
C) Symmetric with respect to the polar axis   ​   
D) Symmetric with respect to the polar axis   ​   
E) Symmetric with respect to the polar axis   ​   
A) Symmetric with respect to the polar axis   ​   
B) Symmetric with respect to the polar axis   ​   
C) Symmetric with respect to the polar axis   ​   
D) Symmetric with respect to the polar axis   ​   
E) Symmetric with respect to the polar axis   ​

Question 2

Give the standard form of the equation of the parabola with the given characteristics. vertex: (-7, -2) focus: (-5, -2)

Accepted Answer

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

Question 3

Select the graph of the following equation. ​   ​

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(s) and vertex at the origin. ​
Focus: (-4,0)
​

Accepted Answer

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

Question 5

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 6

The equations of a parabola and a tangent line to the parabola are given.Select the correct graph of both equations in the same viewing window. ​
Parabola:   Tangent Line:   ​

Accepted Answer

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

Question 7

Find the standard form of the equation of the ellipse with the given characteristics. ​
Center:   ; a = 2c; Vertices:   , where a - thr semimajor axis, b - semiminor axis and   .
​

Accepted Answer

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

Question 8

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 9

Use a graphing utility to graph the parabola.

Accepted Answer

The answer of Use a graphing utility to graph the...

Question 10

​Determine the angle   through which the axes are rotated.Round your answer to two decimal places.   ​​

Accepted Answer

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

Question 11

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

Accepted Answer

A) Center:   ​   
B) Center: (5, 4) ​   
C) Center: (0, 0)   
D) Center:     ​ 
E) Center: (0, 0)   ​ 
A) Center:   ​   
B) Center: (5, 4) ​   
C) Center: (0, 0)   
D) Center:     ​ 
E) Center: (0, 0)   ​

Question 12

Find the standard form of the equation of the hyperbola with the given characteristics. vertices: (5, -6), (5, -2)
Foci: (5, -7), (5, -1)
​

Accepted Answer

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

Question 13

Select the polar equation of the conic for ​e = 1.0 and identify the conic for the following equation. ​   ​

Accepted Answer

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

Question 14

Find the vertex and focus of the parabola.

Accepted Answer

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

Question 15

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

Accepted Answer

A) Vertex:   ; Focus:   ; Directrix:   
B) Vertex:   ; Focus:   ; Directrix:   
C) Vertex:   ; Focus:   ; Directrix:   
D) Vertex:   ; Focus:   ; Directrix:   
E) Vertex:   ; Focus:   ; Directrix:   
A) Vertex:   ; Focus:   ; Directrix:   
B) Vertex:   ; Focus:   ; Directrix:   
C) Vertex:   ; Focus:   ; Directrix:   
D) Vertex:   ; Focus:   ; Directrix:   
E) Vertex:   ; Focus:   ; Directrix:

Question 16

Write an equation for a cross section of the parabolic ear (used to hear sounds from a distance) shown in the picture.   ​ d = 2.25 inches

Accepted Answer

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

Question 17

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 18

Select the graph of degenerate conic. ​   ​

Accepted Answer

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

Question 19

Describe the graph of the polar equation and find the corresponding rectangular equation.Select the correct graph. ​   ​

Accepted Answer

A) The graph of the polar equation is not evident by simple inspection.Convert to rectangular form first.​   ​   
B) The graph of the polar equation is not evident by simple inspection.Convert to rectangular form first.​   ​   
C) The graph of the polar equation is not evident by simple inspection.Convert to rectangular form first.​   ​   
D) The graph of the polar equation is not evident by simple inspection.Convert to rectangular form first.​   ​   
E) The graph of the polar equation is not evident by simple inspection.Convert to rectangular form first.​   ​   
A) The graph of the polar equation is not evident by simple inspection.Convert to rectangular form first.​   ​   
B) The graph of the polar equation is not evident by simple inspection.Convert to rectangular form first.​   ​   
C) The graph of the polar equation is not evident by simple inspection.Convert to rectangular form first.​   ​   
D) The graph of the polar equation is not evident by simple inspection.Convert to rectangular form first.​   ​   
E) The graph of the polar equation is not evident by simple inspection.Convert to rectangular form first.​   ​

Question 20

Find the standard form of the equation of the hyperbola with the given characteristics and center at the origin. ​
Vertices: (0,±2); asymptotes: y = ±   x
​

Accepted Answer

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

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

Give the standard form of the equation of the parabola with the given characteristics. vertex: (-7, -2) focus: (-5, -2)

Select the graph of the following equation.

Find the standard form of the equation of the parabola with the given characteristic(s) and vertex at the origin. Focus: (-4,0)

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

The equations of a parabola and a tangent line to the parabola are given.Select the correct graph of both equations in the same viewing window. Parabola: Tangent Line:

Find the standard form of the equation of the ellipse with the given characteristics. Center: ; a = 2c; Vertices: , where a - thr semimajor axis, b - semiminor axis and .

Use a graphing utility to graph the parabola.

Determine the angle through which the axes are rotated.Round your answer to two decimal places.

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

Find the standard form of the equation of the hyperbola with the given characteristics. vertices: (5, -6), (5, -2) Foci: (5, -7), (5, -1)

Select the polar equation of the conic for e = 1.0 and identify the conic for the following equation.

Find the vertex and focus of the parabola.

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

Write an equation for a cross section of the parabolic ear (used to hear sounds from a distance) shown in the picture. d = 2.25 inches

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.

Select the graph of degenerate conic.

Describe the graph of the polar equation and find the corresponding rectangular equation.Select the correct graph.

Find the standard form of the equation of the hyperbola with the given characteristics and center at the origin. Vertices: (0,±2); asymptotes: y = ± x

Trigonometry

Analytic-Trigonometry

Additional-Topics-In-Trigonometry

Complex-Numbers

Exponential-And-Logarithmic-Functions

Prerequisites

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Exam 6: Topics-In-Analytic-Geometry

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

Give the standard form of the equation of the parabola with the given characteristics. vertex: (-7, -2) focus: (-5, -2)

Select the graph of the following equation. ​ ​

Find the standard form of the equation of the parabola with the given characteristic(s) and vertex at the origin. ​ Focus: (-4,0) ​

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

The equations of a parabola and a tangent line to the parabola are given.Select the correct graph of both equations in the same viewing window. ​ Parabola: Tangent Line: ​

Find the standard form of the equation of the ellipse with the given characteristics. ​ Center: ; a = 2c; Vertices: , where a - thr semimajor axis, b - semiminor axis and . ​

Use a graphing utility to graph the parabola.

​Determine the angle through which the axes are rotated.Round your answer to two decimal places. ​​

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

Find the standard form of the equation of the hyperbola with the given characteristics. vertices: (5, -6), (5, -2) Foci: (5, -7), (5, -1) ​

Select the polar equation of the conic for ​e = 1.0 and identify the conic for the following equation. ​ ​

Find the vertex and focus of the parabola.

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

Write an equation for a cross section of the parabolic ear (used to hear sounds from a distance) shown in the picture. ​ d = 2.25 inches

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. ​ ​

Select the graph of degenerate conic. ​ ​

Describe the graph of the polar equation and find the corresponding rectangular equation.Select the correct graph. ​ ​

Find the standard form of the equation of the hyperbola with the given characteristics and center at the origin. ​ Vertices: (0,±2); asymptotes: y = ± x ​

Trigonometry

Analytic-Trigonometry

Additional-Topics-In-Trigonometry

Complex-Numbers

Exponential-And-Logarithmic-Functions

Prerequisites

Filters

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

Select the graph of the following equation.

Find the standard form of the equation of the parabola with the given characteristic(s) and vertex at the origin. Focus: (-4,0)

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

The equations of a parabola and a tangent line to the parabola are given.Select the correct graph of both equations in the same viewing window. Parabola: Tangent Line:

Find the standard form of the equation of the ellipse with the given characteristics. Center: ; a = 2c; Vertices: , where a - thr semimajor axis, b - semiminor axis and .

Determine the angle through which the axes are rotated.Round your answer to two decimal places.

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

Find the standard form of the equation of the hyperbola with the given characteristics. vertices: (5, -6), (5, -2) Foci: (5, -7), (5, -1)

Select the polar equation of the conic for e = 1.0 and identify the conic for the following equation.

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

Write an equation for a cross section of the parabolic ear (used to hear sounds from a distance) shown in the picture. d = 2.25 inches

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.

Select the graph of degenerate conic.

Describe the graph of the polar equation and find the corresponding rectangular equation.Select the correct graph.

Find the standard form of the equation of the hyperbola with the given characteristics and center at the origin. Vertices: (0,±2); asymptotes: y = ± x