Question 1

Identify the conic. ​   ​

Accepted Answer

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

Question 2

The revenue R (in dollars) generated by the sale of x units of a digital camera is given by   .Approximate the number of sales that will maximize revenue. ​

Accepted Answer

A) Maximum revenue occurs at   units. 
B) Maximum revenue occurs at   units. 
C) Maximum revenue occurs at   units. 
D) Maximum revenue occurs at   units. 
E) Maximum revenue occurs at   units. 
A) Maximum revenue occurs at   units. 
B) Maximum revenue occurs at   units. 
C) Maximum revenue occurs at   units. 
D) Maximum revenue occurs at   units. 
E) Maximum revenue occurs at   units.

Question 3

Find the center and foci of the ellipse. ​   ​

Accepted Answer

A) center:   ; foci:   
B) center:   ; foci:   
C) center:   ; foci:   
D) center:   ; foci:   
E) center:   ; foci:   
A) center:   ; foci:   
B) center:   ; foci:   
C) center:   ; foci:   
D) center:   ; foci:   
E) center:   ; foci:

Question 4

Use the Quadratic Formula to solve for   . ​   ​

Accepted Answer

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

Question 5

Find a polar equation of the conic with its focus at the pole. ​
Conics
Vertex or vertices
Parabola   ​

Accepted Answer

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

Question 6

Find the equation of the hyperbola with vertices (2, 0), (-2, 0) and focus (4, 0). ​

Accepted Answer

A)    
B)    
C)    
D)    
E) none of these 
A)    
B)    
C)    
D)    
E) none of these

Question 7

Write the equation of the ellipse with foci at (2, 2), (6, 2), and b = 4, where b - semiminor axis. ​

Accepted Answer

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

Question 8

A moving conveyor is built so that it rises 3 meter for each 5 meters of horizontal travel.The conveyor runs between two floors in a factory.The distance between the floors is 4 meters.Find the length of the conveyor.Round your answers to one decimal place. ​

Accepted Answer

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

Question 9

Find the inclination Θ (in degrees) of the line with a slope of m.Round your answer to one decimal places. ​   ​

Accepted Answer

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

Question 10

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 Circle with radius 2.5
​   
B) Symmetric with respect to polar axis Circle with radius 2.5
​   
C) Symmetric with respect to polar axis Circle with radius 2.5
​   
D) Symmetric with respect to polar axis Circle with radius 2.5
​   
E) Symmetric with respect to polar axis Circle with radius 2.5
​   
A) Symmetric with respect to polar axis Circle with radius 2.5
​   
B) Symmetric with respect to polar axis Circle with radius 2.5
​   
C) Symmetric with respect to polar axis Circle with radius 2.5
​   
D) Symmetric with respect to polar axis Circle with radius 2.5
​   
E) Symmetric with respect to polar axis Circle with radius 2.5
​

Question 11

Select the correct graph of the polar equation.Find an interval for   for which the graph is traced only once. ​   ​

Accepted Answer

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

Question 12

Identify the conic by writing the equation in standard form.

Accepted Answer

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

Question 13

Select the graph for following equation. ​   ​

Accepted Answer

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

Question 14

Use the discriminant to classify the graph. ​   ​

Accepted Answer

A) The graph is a hyperbola. 
B) The graph is a line. 
C) The graph is a ellipse or Circle. 
D) The graph is a parabola. 
E) The graph is a cone. 
A) The graph is a hyperbola. 
B) The graph is a line. 
C) The graph is a ellipse or Circle. 
D) The graph is a parabola. 
E) The graph is a cone.

Question 15

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

Accepted Answer

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

Question 16

An elliptical stained-glass insert is to be fitted in a 4ft by 6ft rectangular opening (see figure).   Using the coordinate system shown, find an equation for the ellipse. ​

Accepted Answer

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

Question 17

A satellite in a 100-mile-high circular orbit around Earth has a velocity of approximately 17,500 miles per hour.If this velocity is multiplied by   , the satellite will have the minimum velocity necessary to escape Earth's gravity and will follow a parabolic path with the center of Earth as the focus.(Hints: The radius of Earth is 4000 miles.) ​   Find the distance between the surface of the Earth and the satellite when   .
​

Accepted Answer

A) Distance between surface of Earth and satellite:4496 miles 
B) Distance between surface of Earth and satellite:4322 miles 
C) Distance between surface of Earth and satellite:1286 miles 
D) Distance between surface of Earth and satellite:643 miles 
E) Distance between surface of Earth and satellite:1492 miles 
A) Distance between surface of Earth and satellite:4496 miles 
B) Distance between surface of Earth and satellite:4322 miles 
C) Distance between surface of Earth and satellite:1286 miles 
D) Distance between surface of Earth and satellite:643 miles 
E) Distance between surface of Earth and satellite:1492 miles

Question 18

Find the standard form of the equation of the ellipse with the following characteristics. ​
Foci:   , major axis of length: 16
​

Accepted Answer

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

Question 19

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. ​
Horizontal axis and passes through the point   ​

Accepted Answer

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

Question 20

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

Accepted Answer

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

Identify the conic.

The revenue R (in dollars) generated by the sale of x units of a digital camera is given by .Approximate the number of sales that will maximize revenue.

Find the center and foci of the ellipse.

Use the Quadratic Formula to solve for .

Find a polar equation of the conic with its focus at the pole. Conics Vertex or vertices Parabola

Find the equation of the hyperbola with vertices (2, 0), (-2, 0) and focus (4, 0).

Write the equation of the ellipse with foci at (2, 2), (6, 2), and b = 4, where b - semiminor axis.

A moving conveyor is built so that it rises 3 meter for each 5 meters of horizontal travel.The conveyor runs between two floors in a factory.The distance between the floors is 4 meters.Find the length of the conveyor.Round your answers to one decimal place.

Find the inclination Θ (in degrees) of the line with a slope of m.Round your answer to one decimal places.

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

Select the correct graph of the polar equation.Find an interval for for which the graph is traced only once.

Identify the conic by writing the equation in standard form.

Select the graph for following equation.

Use the discriminant to classify the graph.

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

An elliptical stained-glass insert is to be fitted in a 4ft by 6ft rectangular opening (see figure). Using the coordinate system shown, find an equation for the ellipse.

Find the standard form of the equation of the ellipse with the following characteristics. Foci: , major axis of length: 16

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. Horizontal axis and passes through the point

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

Trigonometry

Analytic-Trigonometry

Additional-Topics-In-Trigonometry

Complex-Numbers

Exponential-And-Logarithmic-Functions

Prerequisites

Filters

Exam 6: Topics-In-Analytic-Geometry

Identify the conic. ​ ​

The revenue R (in dollars) generated by the sale of x units of a digital camera is given by .Approximate the number of sales that will maximize revenue. ​

Find the center and foci of the ellipse. ​ ​

Use the Quadratic Formula to solve for . ​ ​

Find a polar equation of the conic with its focus at the pole. ​ Conics Vertex or vertices Parabola ​

Find the equation of the hyperbola with vertices (2, 0), (-2, 0) and focus (4, 0). ​

Write the equation of the ellipse with foci at (2, 2), (6, 2), and b = 4, where b - semiminor axis. ​

A moving conveyor is built so that it rises 3 meter for each 5 meters of horizontal travel.The conveyor runs between two floors in a factory.The distance between the floors is 4 meters.Find the length of the conveyor.Round your answers to one decimal place. ​

Find the inclination Θ (in degrees) of the line with a slope of m.Round your answer to one decimal places. ​ ​

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

Select the correct graph of the polar equation.Find an interval for for which the graph is traced only once. ​ ​

Identify the conic by writing the equation in standard form.

Select the graph for following equation. ​ ​

Use the discriminant to classify the graph. ​ ​

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

An elliptical stained-glass insert is to be fitted in a 4ft by 6ft rectangular opening (see figure). Using the coordinate system shown, find an equation for the ellipse. ​

Find the standard form of the equation of the ellipse with the following characteristics. ​ Foci: , major axis of length: 16 ​

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. ​ Horizontal axis and passes through the point ​

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

Trigonometry

Analytic-Trigonometry

Additional-Topics-In-Trigonometry

Complex-Numbers

Exponential-And-Logarithmic-Functions

Prerequisites

Filters

Identify the conic.

The revenue R (in dollars) generated by the sale of x units of a digital camera is given by .Approximate the number of sales that will maximize revenue.

Find the center and foci of the ellipse.

Use the Quadratic Formula to solve for .

Find a polar equation of the conic with its focus at the pole. Conics Vertex or vertices Parabola

Find the equation of the hyperbola with vertices (2, 0), (-2, 0) and focus (4, 0).

Write the equation of the ellipse with foci at (2, 2), (6, 2), and b = 4, where b - semiminor axis.

A moving conveyor is built so that it rises 3 meter for each 5 meters of horizontal travel.The conveyor runs between two floors in a factory.The distance between the floors is 4 meters.Find the length of the conveyor.Round your answers to one decimal place.

Find the inclination Θ (in degrees) of the line with a slope of m.Round your answer to one decimal places.

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

Select the correct graph of the polar equation.Find an interval for for which the graph is traced only once.

Select the graph for following equation.

Use the discriminant to classify the graph.

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

An elliptical stained-glass insert is to be fitted in a 4ft by 6ft rectangular opening (see figure). Using the coordinate system shown, find an equation for the ellipse.

Find the standard form of the equation of the ellipse with the following characteristics. Foci: , major axis of length: 16

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. Horizontal axis and passes through the point