Question 1

Find the vertex and directrix of the parabola.

Accepted Answer

A) vertex:   directrix:   
B) vertex:   directrix:   
C) vertex:   directrix:   
D) vertex:   directrix:   
E) vertex:   directrix:   
A) vertex:   directrix:   
B) vertex:   directrix:   
C) vertex:   directrix:   
D) vertex:   directrix:   
E) vertex:   directrix:

Question 2

The revenue (in dollars) generated by the sale of units of a patio furniture set is given by   .Select the correct graph of the function. ​

Accepted Answer

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

Question 3

The Falls Incline Railway in Niagara Falls, Ontario, Canada is an inclined railway that was designed to carry people from the City of Niagara Falls to Queen Victoria Park.The railway is approximately 180 feet long with a 42% uphill grade (see figure).Select the graph of the equation of the line that models the railway track. ​   ​   ​

Accepted Answer

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

Question 4

Convert the polar equation to rectangular form. ​   ​

Accepted Answer

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

Question 5

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 6

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

Question 7

Find the rectangular coordinates of the point given in polar coordinates.Round your results to two decimal places. ​   ​

Accepted Answer

A) Rectangular coordinates: (7.61,0.07) 
B) Rectangular coordinates: (7.61,-7.61) 
C) Rectangular coordinates: (-2.47,-7.61) 
D) Rectangular coordinates: (-2.47,7.61) 
E) Rectangular coordinates: (-2.47,0.07) 
A) Rectangular coordinates: (7.61,0.07) 
B) Rectangular coordinates: (7.61,-7.61) 
C) Rectangular coordinates: (-2.47,-7.61) 
D) Rectangular coordinates: (-2.47,7.61) 
E) Rectangular coordinates: (-2.47,0.07)

Question 8

Use the following results the polar equation of the ellipse   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 9

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 10

Use the Quadratic Formula to solve for   . ​   ​

Accepted Answer

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

Question 11

Identify the conic. ​   ​

Accepted Answer

A) Ellipse 
B) Circle 
C) Parabola 
D) Line 
E) Hyperbola 
A) Ellipse 
B) Circle 
C) Parabola 
D) Line 
E) Hyperbola

Question 12

Find the standard form of the equation of the hyperbola with the given characteristics. vertices: (-10, -2), (0, -2)
Asymptotes: y = ±   x
​

Accepted Answer

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

Question 13

Find the slope of the line with inclination   .Round your answer to four decimal places. ​   ​
​

Accepted Answer

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

Question 14

Find the Foci of the conic. ​   ​

Accepted Answer

A) Foci:   
B) Foci:   
C) Foci:   
D) Foci:   
E) Foci:   
A) Foci:   
B) Foci:   
C) Foci:   
D) Foci:   
E) Foci:

Question 15

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 16

Find the vertex and focus of the parabola.

Accepted Answer

A) vertex:   focus:   
B) vertex:   focus:   
C) vertex:   focus:   
D) vertex:   focus:   
E) vertex:   focus:   
A) vertex:   focus:   
B) vertex:   focus:   
C) vertex:   focus:   
D) vertex:   focus:   
E) vertex:   focus:

Question 17

Consider a line with slope m and y-intercept (0,7).Select the graph of the distance between the origin and the line. ​

Accepted Answer

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

Question 18

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 19

Find the center and radius of the conic. ​   ​

Accepted Answer

A) Center:   Radius:   
B) Center:   Radius:   
C) Center: (0,0) Radius:   
D) Center:   Radius:   
E) Center:   Radius:   
A) Center:   Radius:   
B) Center:   Radius:   
C) Center: (0,0) Radius:   
D) Center:   Radius:   
E) Center:   Radius:

Question 20

Find the distance between the point and the line.Round your answer to four decimal places. ​   ​

Accepted Answer

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

Find the vertex and directrix of the parabola.

The revenue (in dollars) generated by the sale of units of a patio furniture set is given by .Select the correct graph of the function.

Convert the polar equation to rectangular form.

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

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

Find the rectangular coordinates of the point given in polar coordinates.Round your results to two decimal places.

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

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

Use the Quadratic Formula to solve for .

Identify the conic.

Find the standard form of the equation of the hyperbola with the given characteristics. vertices: (-10, -2), (0, -2) Asymptotes: y = ± x

Find the slope of the line with inclination .Round your answer to four decimal places.

Find the Foci of the conic.

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.

Find the vertex and focus of the parabola.

Consider a line with slope m and y-intercept (0,7).Select the graph of the distance between the origin and the line.

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

Find the center and radius of the conic.

Find the distance between the point and the line.Round your answer to four decimal places.

Trigonometry

Analytic-Trigonometry

Additional-Topics-In-Trigonometry

Complex-Numbers

Exponential-And-Logarithmic-Functions

Prerequisites

Filters

Exam 6: Topics-In-Analytic-Geometry

Find the vertex and directrix of the parabola.

The revenue (in dollars) generated by the sale of units of a patio furniture set is given by .Select the correct graph of the function. ​

Convert the polar equation to rectangular form. ​ ​

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

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

Find the rectangular coordinates of the point given in polar coordinates.Round your results to two decimal places. ​ ​

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

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

Use the Quadratic Formula to solve for . ​ ​

Identify the conic. ​ ​

Find the standard form of the equation of the hyperbola with the given characteristics. vertices: (-10, -2), (0, -2) Asymptotes: y = ± x ​

Find the slope of the line with inclination .Round your answer to four decimal places. ​ ​ ​

Find the Foci of the conic. ​ ​

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. ​ ​

Find the vertex and focus of the parabola.

Consider a line with slope m and y-intercept (0,7).Select the graph of the distance between the origin and the line. ​

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

Find the center and radius of the conic. ​ ​

Find the distance between the point and the line.Round your answer to four decimal places. ​ ​

Trigonometry

Analytic-Trigonometry

Additional-Topics-In-Trigonometry

Complex-Numbers

Exponential-And-Logarithmic-Functions

Prerequisites

Filters

The revenue (in dollars) generated by the sale of units of a patio furniture set is given by .Select the correct graph of the function.

Convert the polar equation to rectangular form.

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

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

Find the rectangular coordinates of the point given in polar coordinates.Round your results to two decimal places.

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

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

Use the Quadratic Formula to solve for .

Identify the conic.

Find the standard form of the equation of the hyperbola with the given characteristics. vertices: (-10, -2), (0, -2) Asymptotes: y = ± x

Find the slope of the line with inclination .Round your answer to four decimal places.

Find the Foci of the conic.

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.

Consider a line with slope m and y-intercept (0,7).Select the graph of the distance between the origin and the line.

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

Find the center and radius of the conic.

Find the distance between the point and the line.Round your answer to four decimal places.