Question 1

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

Accepted Answer

A) Rectangular coordinates: (2.27,-7.89) 
B) Rectangular coordinates: (-7.89,2.27) 
C) Rectangular coordinates: (1.27,-8.89) 
D) Rectangular coordinates: (-8.89,1.27) 
E) Rectangular coordinates: (8.98,4.50) 
A) Rectangular coordinates: (2.27,-7.89) 
B) Rectangular coordinates: (-7.89,2.27) 
C) Rectangular coordinates: (1.27,-8.89) 
D) Rectangular coordinates: (-8.89,1.27) 
E) Rectangular coordinates: (8.98,4.50)

Question 2

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 3

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

Accepted Answer

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

Question 4

Select the correct equation of the following graph. ​
​   ​

Accepted Answer

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

Question 5

Use the Quadratic Formula to solve for   . ​   ​

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

Question 7

Find the standard form of the equation of the parabola with the given characteristic(s) and vertex at the origin. ​
Directrix: y = 2
​

Accepted Answer

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

Question 8

Consider the equation   .Select the correct graph of the equation for   . ​

Accepted Answer

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

Question 9

Roads are often designed with parabolic surfaces to allow rain to drain off.A particular road that is 44 feet wide is 0.4 foot higher in the center than it is on the sides (see figure). ​   ​
Where   ft,   ​
Find an equation of the parabola that models the road surface.(Assume that the origin is at the center of the road.)
​

Accepted Answer

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

Question 10

Identify the conic and select its correct graph. ​   ​

Accepted Answer

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

Question 11

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

Accepted Answer

A) Rectangular coordinates: (4.89,0.350) 
B) Rectangular coordinates: (4.89,0.35) 
C) Rectangular coordinates: (0.35,4.890) 
D) Rectangular coordinates: (0.35,4.89) 
E) Rectangular coordinates: (5,1.5) 
A) Rectangular coordinates: (4.89,0.350) 
B) Rectangular coordinates: (4.89,0.35) 
C) Rectangular coordinates: (0.35,4.890) 
D) Rectangular coordinates: (0.35,4.89) 
E) Rectangular coordinates: (5,1.5)

Question 12

Select the graph of the following equation, showing both sets of axes. ​   ​

Accepted Answer

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

Question 13

Select correct graph to graph rotated conic. ​   ​

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:   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 15

Use the Quadratic Formula to solve for   . ​   ​

Accepted Answer

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

Question 16

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

Accepted Answer

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

Question 17

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

Question 18

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

Accepted Answer

A)    The revenue is maximum when   units. 
B)    The revenue is maximum when   units. 
C)    The revenue is maximum when   units. 
D)    The revenue is maximum when   units. 
E)    The revenue is maximum when   units. 
A)    The revenue is maximum when   units. 
B)    The revenue is maximum when   units. 
C)    The revenue is maximum when   units. 
D)    The revenue is maximum when   units. 
E)    The revenue is maximum when   units.

Question 19

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 20

Use the discriminant to classify the graph. ​   ​

Accepted Answer

A) The graph is a cone. 
B) The graph is a circle. 
C) The graph is a parabola. 
D) The graph is a ellipse. 
E) The graph is a hyperbola. 
A) The graph is a cone. 
B) The graph is a circle. 
C) The graph is a parabola. 
D) The graph is a ellipse. 
E) The graph is a hyperbola.

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

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.

Select the correct equation of the following graph.

Use the Quadratic Formula to solve for .

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 parabola with the given characteristic(s) and vertex at the origin. Directrix: y = 2

Consider the equation .Select the correct graph of the equation for .

Identify the conic and select its correct graph.

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

Select the graph of the following equation, showing both sets of axes.

Select correct graph to graph rotated conic.

Find the vertex and focus of the parabola.

Use the Quadratic Formula to solve for .

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

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

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

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

Use the discriminant to classify the graph.

Trigonometry

Analytic-Trigonometry

Additional-Topics-In-Trigonometry

Complex-Numbers

Exponential-And-Logarithmic-Functions

Prerequisites

Filters

Exam 6: Topics-In-Analytic-Geometry

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

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. ​ ​

Select the correct equation of the following graph. ​ ​ ​

Use the Quadratic Formula to solve for . ​ ​

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 parabola with the given characteristic(s) and vertex at the origin. ​ Directrix: y = 2 ​

Consider the equation .Select the correct graph of the equation for . ​

Identify the conic and select its correct graph. ​ ​

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

Select the graph of the following equation, showing both sets of axes. ​ ​

Select correct graph to graph rotated conic. ​ ​

Find the vertex and focus of the parabola.

Use the Quadratic Formula to solve for . ​ ​

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

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

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

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

Use the discriminant to classify the graph. ​ ​

Trigonometry

Analytic-Trigonometry

Additional-Topics-In-Trigonometry

Complex-Numbers

Exponential-And-Logarithmic-Functions

Prerequisites

Filters

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

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.

Select the correct equation of the following graph.

Use the Quadratic Formula to solve for .

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 parabola with the given characteristic(s) and vertex at the origin. Directrix: y = 2

Consider the equation .Select the correct graph of the equation for .

Identify the conic and select its correct graph.

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

Select the graph of the following equation, showing both sets of axes.

Select correct graph to graph rotated conic.

Use the Quadratic Formula to solve for .

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

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

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

Use the discriminant to classify the graph.