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     ​   
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 2

A point (a,b) = (r, θ) shown in below graph in polar coordinates is given.Convert the point to rectangular coordinates. ​   ​   ​

Accepted Answer

A) Rectangular coordinates: (5,0) 
B) Rectangular coordinates: (5,5) 
C) Rectangular coordinates: (-5,5) 
D) Rectangular coordinates: (-5,0) 
E) Rectangular coordinates: (0,5) 
A) Rectangular coordinates: (5,0) 
B) Rectangular coordinates: (5,5) 
C) Rectangular coordinates: (-5,5) 
D) Rectangular coordinates: (-5,0) 
E) Rectangular coordinates: (0,5)

Question 3

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 4

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

Accepted Answer

A) x2 = -16y 
B) x2 = -4y 
C) x2 = 4y 
D) y2 = -16x 
E) y2 = -4x 
A) x2 = -16y 
B) x2 = -4y 
C) x2 = 4y 
D) y2 = -16x 
E) y2 = -4x

Question 5

Write the equation of the ellipse that has its center at the origin with focus at (0, 1) and vertex at (0, 11). ​

Accepted Answer

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

Question 6

Use a graphing utility to graph the conic.Determine the angle   through which the axes are rotated. ​   ​

Accepted Answer

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

Question 7

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

Accepted Answer

A) Center: (-3, 5) ​   
B) Center: (0, 0)   ​ 
C) Center: (3, - 5)   
D) Center: (0, 0)   
E) Center: (3, 5)   
A) Center: (-3, 5) ​   
B) Center: (0, 0)   ​ 
C) Center: (3, - 5)   
D) Center: (0, 0)   
E) Center: (3, 5)

Question 8

Find the vertices and asymptotes of the hyperbola.

Accepted Answer

A) vertices: (0, ±8) asymptote: y = ±   x 
B) vertices: (0, ±8) asymptote: y = ±   x 
C) vertices: (±8, 0) asymptote: y = ±   x 
D) vertices: (±8, 0) asymptote: y = ±   x 
E) vertices: (±8, 9) asymptote: y = ±   x 
A) vertices: (0, ±8) asymptote: y = ±   x 
B) vertices: (0, ±8) asymptote: y = ±   x 
C) vertices: (±8, 0) asymptote: y = ±   x 
D) vertices: (±8, 0) asymptote: y = ±   x 
E) vertices: (±8, 9) asymptote: y = ±   x

Question 9

As a speeding train crosses a trestle over a deep gorge, a child drops his toy plane from the window.The path of the toy plane is modeled by   , where y is the height above the floor of the gorge and distances are measured in feet.How far will the toy plane travel horizontally before it hits the bottom of the gorge? [Note: The toy plane does not glide; it "drops like a rock."]

Accepted Answer

A) 7.0 ft 
B) 36.0 ft 
C) 185 ft 
D) 1295.0 ft 
E) 14 ft 
A) 7.0 ft 
B) 36.0 ft 
C) 185 ft 
D) 1295.0 ft 
E) 14 ft

Question 10

Select the graph of degenerate conic. ​   ​

Accepted Answer

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

Question 11

Select the polar equation of graph. ​   ​

Accepted Answer

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

Question 12

Find the vertex and focus of the parabola for the given equation and select its graph. ​   ​

Accepted Answer

A) Vertex: (0,0) Focus: (1,0)   
B) Vertex: (0,0) Focus: (1,0)   
C) Vertex: (0,0) Focus: (-1,0)   
D) Vertex: (0,0) Focus: (   1,0)   
E) Vertex: (0,0) Focus: (0,1)   
A) Vertex: (0,0) Focus: (1,0)   
B) Vertex: (0,0) Focus: (1,0)   
C) Vertex: (0,0) Focus: (-1,0)   
D) Vertex: (0,0) Focus: (   1,0)   
E) Vertex: (0,0) Focus: (0,1)

Question 13

The revenue R (in dollars) generated by the sale of x 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 14

Find the standard form of the equation of the hyperbola with the given characteristics. ​
Vertices: (6, 0),(10, 0); foci: (0, 0), (12, 0)
​

Accepted Answer

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

Question 15

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 16

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 17

Select the curve represented by the parametric equations. ​
Prolate cycloid:   ​

Accepted Answer

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

Question 18

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

Accepted Answer

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

Question 19

Give the coordinates of the circle's center and its radius. ​   ​

Accepted Answer

A) (1, 1); r = 64 
B) (0, 0); r = 8 
C) (1, 1); r = 8 
D) (0, 0); r = 64 
E) none of these 
A) (1, 1); r = 64 
B) (0, 0); r = 8 
C) (1, 1); r = 8 
D) (0, 0); r = 64 
E) none of these

Question 20

Find the standard form of the equation of the ellipse with vertices   and eccentricity   .

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.

A point (a,b) = (r, θ) shown in below graph in polar coordinates is given.Convert the point to rectangular coordinates.

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

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

Write the equation of the ellipse that has its center at the origin with focus at (0, 1) and vertex at (0, 11).

Use a graphing utility to graph the conic.Determine the angle through which the axes are rotated.

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

Find the vertices and asymptotes of the hyperbola.

Select the graph of degenerate conic.

Select the polar equation of graph.

Find the vertex and focus of the parabola for the given equation and select its graph.

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

Find the standard form of the equation of the hyperbola with the given characteristics. Vertices: (6, 0),(10, 0); foci: (0, 0), (12, 0)

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

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

Select the curve represented by the parametric equations. Prolate cycloid:

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

Give the coordinates of the circle's center and its radius.

Find the standard form of the equation of the ellipse with vertices and eccentricity .

Trigonometry

Analytic-Trigonometry

Additional-Topics-In-Trigonometry

Complex-Numbers

Exponential-And-Logarithmic-Functions

Prerequisites

Filters

Exam 6: Topics-In-Analytic-Geometry

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

A point (a,b) = (r, θ) shown in below graph in polar coordinates is given.Convert the point to rectangular coordinates. ​ ​ ​

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

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

Write the equation of the ellipse that has its center at the origin with focus at (0, 1) and vertex at (0, 11). ​

Use a graphing utility to graph the conic.Determine the angle through which the axes are rotated. ​ ​

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

Find the vertices and asymptotes of the hyperbola.

Select the graph of degenerate conic. ​ ​

Select the polar equation of graph. ​ ​

Find the vertex and focus of the parabola for the given equation and select its graph. ​ ​

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

Find the standard form of the equation of the hyperbola with the given characteristics. ​ Vertices: (6, 0),(10, 0); foci: (0, 0), (12, 0) ​

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

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

Select the curve represented by the parametric equations. ​ Prolate cycloid: ​

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

Give the coordinates of the circle's center and its radius. ​ ​

Find the standard form of the equation of the ellipse with vertices and eccentricity .

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.

A point (a,b) = (r, θ) shown in below graph in polar coordinates is given.Convert the point to rectangular coordinates.

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

Write the equation of the ellipse that has its center at the origin with focus at (0, 1) and vertex at (0, 11).

Use a graphing utility to graph the conic.Determine the angle through which the axes are rotated.

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

Select the graph of degenerate conic.

Select the polar equation of graph.

Find the vertex and focus of the parabola for the given equation and select its graph.

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

Find the standard form of the equation of the hyperbola with the given characteristics. Vertices: (6, 0),(10, 0); foci: (0, 0), (12, 0)

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

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

Select the curve represented by the parametric equations. Prolate cycloid:

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

Give the coordinates of the circle's center and its radius.