Question 1

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. directrix: x = 5

Accepted Answer

A) x2 = -20y 
B) x2 = 20y 
C) x2 = 5y 
D) y2 = 5x 
E) y2 = -20x 
A) x2 = -20y 
B) x2 = 20y 
C) x2 = 5y 
D) y2 = 5x 
E) y2 = -20x

Question 2

Select the parametric equations matching with the following graph. ​   ​

Accepted Answer

A) Lissajous curve:   
B) Lissajous curve:   
C) Lissajous curve:   
D) Lissajous curve:   , 
E) Lissajous curve:   
A) Lissajous curve:   
B) Lissajous curve:   
C) Lissajous curve:   
D) Lissajous curve:   , 
E) Lissajous curve:

Question 3

Graph the following equation. ​   ​

Accepted Answer

A) ​   
B) ​   
C) ​   
A) ​   
B) ​   
C) ​

Question 4

Find the center and foci of the ellipse. ​   ​

Accepted Answer

A) center: (-7, -2); foci: (-7, -5), (-7, 1) 
B) center: (7, 2); foci: (-10, -2), (-4, -2) 
C) center: (-7, -2); foci: (-10, 2), (-4, 2) 
D) center: (7, 2); foci: (7, -1), (7, 5) 
E) center: (7, 2); foci: (4, 2), (10, 2) 
A) center: (-7, -2); foci: (-7, -5), (-7, 1) 
B) center: (7, 2); foci: (-10, -2), (-4, -2) 
C) center: (-7, -2); foci: (-10, 2), (-4, 2) 
D) center: (7, 2); foci: (7, -1), (7, 5) 
E) center: (7, 2); foci: (4, 2), (10, 2)

Question 5

Convert the polar equation to rectangular form. ​   ​

Accepted Answer

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

Question 6

Find the vertices of the conic. ​   ​

Accepted Answer

A) Vertices:   
B) Vertices:   
C) Vertices:   
D) Vertices:   
E) Vertices:   
A) Vertices:   
B) Vertices:   
C) Vertices:   
D) Vertices:   
E) Vertices:

Question 7

Find the center and vertices which located on the major axis of the ellipse from given equation and select its graph. ​   ​

Accepted Answer

A) Center: (0,0) Vertices: (±10,0)
​   
B) Center: (0,0) Vertices: (10,0)   
C) Center: (0,0) Vertices: (-10,0)
​   
D) Center: (0,0) Vertices: (-10,0)
​   
E) Center: (0,0) Vertices: (±10,0)
​   
A) Center: (0,0) Vertices: (±10,0)
​   
B) Center: (0,0) Vertices: (10,0)   
C) Center: (0,0) Vertices: (-10,0)
​   
D) Center: (0,0) Vertices: (-10,0)
​   
E) Center: (0,0) Vertices: (±10,0)
​

Question 8

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 9

Select the correct equation of the following graph. ​   ​

Accepted Answer

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

Question 10

Use the discriminant to classify the graph. ​   ​

Accepted Answer

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

Question 11

Find the standard form of the equation of the hyperbola with the given characteristics. vertices: (0,±4) focies: (0,±5)

Accepted Answer

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

Question 12

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

Accepted Answer

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

Question 13

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

Accepted Answer

A) Vertex: (0,0) Focus: (0,3)   
B) Vertex: (0,0) Focus: (0,-12)   
C) Vertex: (0,0) Focus: (0,-3)   
D) Vertex: (0,0) Focus:     
E) Vertex: (0,0) Focus:     
A) Vertex: (0,0) Focus: (0,3)   
B) Vertex: (0,0) Focus: (0,-12)   
C) Vertex: (0,0) Focus: (0,-3)   
D) Vertex: (0,0) Focus:     
E) Vertex: (0,0) Focus:

Question 14

By using a graphing utility select the correct graph of the polar equation.Identify the graph. ​   ​

Accepted Answer

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

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

Find the standard form of the equation of the parabola with the given characteristic(s) and vertex at the origin. ​
Passes through the point (2,4); horizontal axis
​

Accepted Answer

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

Question 17

Consider a line with slope m and y-intercept (0,8).Write the distance d between the point (7,1) and the line as a function of m. ​

Accepted Answer

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

Question 18

Find the equation of the parabola so that its graph matches the description. ​   ; upper half of parabola
​

Accepted Answer

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

Question 19

Rotate the axes to eliminate the xy-term in the equation.Then write the equation in standard form. ​   ​

Accepted Answer

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

Question 20

Find the vertices and asymptotes of the hyperbola. ​   ​

Accepted Answer

A) ​vertices: (0, ±3) asymptote:   
B) ​​vertices: (0, ±3) asymptote:   
C) ​vertices: (±3, 0) asymptote:   
D) ​​vertices: (±3, 0) asymptote:   
E) ​vertices: (±3, 4) asymptote:   
A) ​vertices: (0, ±3) asymptote:   
B) ​​vertices: (0, ±3) asymptote:   
C) ​vertices: (±3, 0) asymptote:   
D) ​​vertices: (±3, 0) asymptote:   
E) ​vertices: (±3, 4) asymptote:

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. directrix: x = 5

Select the parametric equations matching with the following graph.

Graph the following equation.

Find the center and foci of the ellipse.

Convert the polar equation to rectangular form.

Find the vertices of the conic.

Find the center and vertices which located on the major axis of the ellipse from given equation and select its graph.

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

Select the correct equation of the following graph.

Use the discriminant to classify the graph.

Find the standard form of the equation of the hyperbola with the given characteristics. vertices: (0,±4) focies: (0,±5)

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

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

By using a graphing utility select the correct graph of the polar equation.Identify the graph.

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

Find the standard form of the equation of the parabola with the given characteristic(s) and vertex at the origin. Passes through the point (2,4); horizontal axis

Consider a line with slope m and y-intercept (0,8).Write the distance d between the point (7,1) and the line as a function of m.

Find the equation of the parabola so that its graph matches the description. ; upper half of parabola

Rotate the axes to eliminate the xy-term in the equation.Then write the equation in standard form.

Find the vertices and asymptotes of the hyperbola.

Trigonometry

Analytic-Trigonometry

Additional-Topics-In-Trigonometry

Complex-Numbers

Exponential-And-Logarithmic-Functions

Prerequisites

Filters

Exam 6: Topics-In-Analytic-Geometry

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. directrix: x = 5

Select the parametric equations matching with the following graph. ​ ​

Graph the following equation. ​ ​

Find the center and foci of the ellipse. ​ ​

Convert the polar equation to rectangular form. ​ ​

Find the vertices of the conic. ​ ​

Find the center and vertices which located on the major axis of the ellipse from given equation and select its graph. ​ ​

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

Select the correct equation of the following graph. ​ ​

Use the discriminant to classify the graph. ​ ​

Find the standard form of the equation of the hyperbola with the given characteristics. vertices: (0,±4) focies: (0,±5)

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

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

By using a graphing utility select the correct graph of the polar equation.Identify the graph. ​ ​

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

Find the standard form of the equation of the parabola with the given characteristic(s) and vertex at the origin. ​ Passes through the point (2,4); horizontal axis ​

Consider a line with slope m and y-intercept (0,8).Write the distance d between the point (7,1) and the line as a function of m. ​

Find the equation of the parabola so that its graph matches the description. ​ ; upper half of parabola ​

Rotate the axes to eliminate the xy-term in the equation.Then write the equation in standard form. ​ ​

Find the vertices and asymptotes of the hyperbola. ​ ​

Trigonometry

Analytic-Trigonometry

Additional-Topics-In-Trigonometry

Complex-Numbers

Exponential-And-Logarithmic-Functions

Prerequisites

Filters

Select the parametric equations matching with the following graph.

Graph the following equation.

Find the center and foci of the ellipse.

Convert the polar equation to rectangular form.

Find the vertices of the conic.

Find the center and vertices which located on the major axis of the ellipse from given equation and select its graph.

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

Select the correct equation of the following graph.

Use the discriminant to classify the graph.

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

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

By using a graphing utility select the correct graph of the polar equation.Identify the graph.

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

Find the standard form of the equation of the parabola with the given characteristic(s) and vertex at the origin. Passes through the point (2,4); horizontal axis

Consider a line with slope m and y-intercept (0,8).Write the distance d between the point (7,1) and the line as a function of m.

Find the equation of the parabola so that its graph matches the description. ; upper half of parabola

Rotate the axes to eliminate the xy-term in the equation.Then write the equation in standard form.

Find the vertices and asymptotes of the hyperbola.