Question 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   ; vertical axis
​

Accepted Answer

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

Question 2

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 3

Match the equation with its graph.

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

Find the center, vertices and foci of the hyperbola. ​   ​

Accepted Answer

A) Center: (0, 0) Vertices:  
Foci:   
B) Center: (0, 0) Vertices:  
Foci:   
C) Center:   Vertices:  
Foci:   
D) Center:   Vertices:  
Foci:   
E) Center: (0, 0) Vertices:  
Foci:   
A) Center: (0, 0) Vertices:  
Foci:   
B) Center: (0, 0) Vertices:  
Foci:   
C) Center:   Vertices:  
Foci:   
D) Center:   Vertices:  
Foci:   
E) Center: (0, 0) Vertices:  
Foci:

Question 6

Select the curve represented by the parametric equations. ​     ​

Accepted Answer

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

Question 7

Find the center and vertices of the ellipse. ​   ​

Accepted Answer

A) center: (-1, 3), vertices: (-3, 3), (1, 3) 
B) center: (-3, 1), vertices: (-4, 1), (-2, 1) 
C) center: (3, -1), vertices: (2, -1), (4, -1) 
D) center: (3, -1), vertices: (1, -1), (5, -1) 
E) center: (-3, 1), vertices: (-5, 1), (-1, 1) 
A) center: (-1, 3), vertices: (-3, 3), (1, 3) 
B) center: (-3, 1), vertices: (-4, 1), (-2, 1) 
C) center: (3, -1), vertices: (2, -1), (4, -1) 
D) center: (3, -1), vertices: (1, -1), (5, -1) 
E) center: (-3, 1), vertices: (-5, 1), (-1, 1)

Question 8

A projectile is launched at a height of h feet above the ground at an angle of   with the horizontal.The initial velocity is   feet per second, and the path of the projectile is modeled by the parametric equations   . Select the correct graph of the path of a projectile launched from ground level at the value of   and   .
​   ,   feet per second
​

Accepted Answer

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

Question 9

Find the center, vertices and foci of the hyperbola. ​   ​

Accepted Answer

A) Center: (1, 1) Vertices:  
Foci:   
B) Center:   Vertices:  
Foci:   
C) Center: (0, 0) Vertices:  
Foci:   
D) Center: (0, 0) Vertices:  
Foci:   
E) Center:   Vertices:  
Foci:   
A) Center: (1, 1) Vertices:  
Foci:   
B) Center:   Vertices:  
Foci:   
C) Center: (0, 0) Vertices:  
Foci:   
D) Center: (0, 0) Vertices:  
Foci:   
E) Center:   Vertices:  
Foci:

Question 10

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 11

Find the center, vertices and foci of the hyperbola. ​   ​

Accepted Answer

A) Center: (0, 0) Vertices:  
Foci:   
B) Center: (0, 0) Vertices:  
Foci:   
C) Center: (0, 0) Vertices:  
Foci:   
D) Center: (0, 0) Vertices:  
Foci:   
E) Center: (0, 0) Vertices:  
Foci:   
A) Center: (0, 0) Vertices:  
Foci:   
B) Center: (0, 0) Vertices:  
Foci:   
C) Center: (0, 0) Vertices:  
Foci:   
D) Center: (0, 0) Vertices:  
Foci:   
E) Center: (0, 0) Vertices:  
Foci:

Question 12

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 13

A point in rectangular coordinates is given.Convert the point to polar coordinates, r > 0. ​   ​

Accepted Answer

A) Polar coordinates:   
B) Polar coordinates:   
C) Polar coordinates:   
D) Polar coordinates:   
E) Polar coordinates:   
A) Polar coordinates:   
B) Polar coordinates:   
C) Polar coordinates:   
D) Polar coordinates:   
E) Polar coordinates:

Question 14

Using following result find a set of parametric equation of the line. ​   ​
Line: passes through   and   ​

Accepted Answer

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

Question 15

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

Accepted Answer

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

Question 16

Select the curve represented by the parametric equations.(indicate the orientation of the curve) ​     ​

Accepted Answer

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

Question 17

Graph the hyperbola. ​   ​

Accepted Answer

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

Question 18

Select the curve represented by the parametric equations. ​     ​

Accepted Answer

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

Question 19

Find the center, vertices and foci of the hyperbola. ​   ​

Accepted Answer

A) Center: (0, 0) Vertices:  
Foci:   
B) Center: (0, 0) Vertices:  
Foci:   
C) Center: (0, 0) Vertices:  
Foci:   
D) Center: (0, 0) Vertices:  
Foci:   
E) Center: (0, 0) Vertices:  
Foci:   
A) Center: (0, 0) Vertices:  
Foci:   
B) Center: (0, 0) Vertices:  
Foci:   
C) Center: (0, 0) Vertices:  
Foci:   
D) Center: (0, 0) Vertices:  
Foci:   
E) Center: (0, 0) Vertices:  
Foci:

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 standard form of the equation of the parabola with the given characteristic(s) and vertex at the origin. Passes through the point ; vertical axis

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

Match the equation with its graph.

Convert the polar equation to rectangular form.

Find the center, vertices and foci of the hyperbola.

Select the curve represented by the parametric equations.

Find the center and vertices of the ellipse.

Find the center, vertices and foci of the hyperbola.

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

Find the center, vertices and foci of the hyperbola.

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

A point in rectangular coordinates is given.Convert the point to polar coordinates, r > 0.

Using following result find a set of parametric equation of the line. Line: passes through and

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.(indicate the orientation of the curve)

Graph the hyperbola.

Select the curve represented by the parametric equations.

Find the center, vertices and foci of the hyperbola.

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 standard form of the equation of the parabola with the given characteristic(s) and vertex at the origin. ​ Passes through the point ; vertical axis ​

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

Match the equation with its graph.

Convert the polar equation to rectangular form. ​ ​

Find the center, vertices and foci of the hyperbola. ​ ​

Select the curve represented by the parametric equations. ​ ​

Find the center and vertices of the ellipse. ​ ​

Find the center, vertices and foci of the hyperbola. ​ ​

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

Find the center, vertices and foci of the hyperbola. ​ ​

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

A point in rectangular coordinates is given.Convert the point to polar coordinates, r > 0. ​ ​

Using following result find a set of parametric equation of the line. ​ ​ Line: passes through and ​

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.(indicate the orientation of the curve) ​ ​

Graph the hyperbola. ​ ​

Select the curve represented by the parametric equations. ​ ​

Find the center, vertices and foci of the hyperbola. ​ ​

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

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

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

Convert the polar equation to rectangular form.

Find the center, vertices and foci of the hyperbola.

Select the curve represented by the parametric equations.

Find the center and vertices of the ellipse.

Find the center, vertices and foci of the hyperbola.

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

Find the center, vertices and foci of the hyperbola.

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

A point in rectangular coordinates is given.Convert the point to polar coordinates, r > 0.

Using following result find a set of parametric equation of the line. Line: passes through and

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.(indicate the orientation of the curve)

Graph the hyperbola.

Select the curve represented by the parametric equations.

Find the center, vertices and foci of the hyperbola.

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