Question 1

Find the standard form of the equation of the hyperbola with the given characteristics and center at the origin. ​
Vertices:   ; asymptotes:   ​

Accepted Answer

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

Question 2

Use the Quadratic Formula to solve for   . ​   ​

Accepted Answer

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

Question 3

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

Accepted Answer

A) Center: (1, 1) Vertices: (±4, 0)
Foci:   ​ 
B) Center:   Vertices: (±4, 0)
Foci:   
C) Center: (0, 0) Vertices: (0, ±   )
Foci:   
D) Center: (1, 1) Vertices: (0, ±   )
Foci:   
E) Center: (0, 0) Vertices: (±   , 0)
Foci:   
A) Center: (1, 1) Vertices: (±4, 0)
Foci:   ​ 
B) Center:   Vertices: (±4, 0)
Foci:   
C) Center: (0, 0) Vertices: (0, ±   )
Foci:   
D) Center: (1, 1) Vertices: (0, ±   )
Foci:   
E) Center: (0, 0) Vertices: (±   , 0)
Foci:

Question 4

Select the correct graph of the polar equation.Describe your viewing window. ​   ​

Accepted Answer

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

Question 5

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 6

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

Accepted Answer

A) Involute of circle:   
B) Involute of circle:   
C) Involute of circle:   
D) Involute of circle:   
E) Involute of circle:   
A) Involute of circle:   
B) Involute of circle:   
C) Involute of circle:   
D) Involute of circle:   
E) Involute of circle:

Question 7

Select the correct graph of the polar equation.Describe your viewing window. ​   ​

Accepted Answer

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

Question 8

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 9

Find the standard form of the equation of the parabola with the given characteristic(s) and vertex at the origin. ​
Focus: (0,   )
​

Accepted Answer

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

Question 10

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 11

Describe the graph of the polar equation and find the corresponding rectangular equation.Select the correct graph. ​   ​

Accepted Answer

A) The graph of the polar equation consists of all points that are two units from the pole.     
B) The graph of the polar equation consists of all points that are two units from the pole.     
C) The graph of the polar equation consists of all points that are two units from the pole.     
D) The graph of the polar equation consists of all points that are two units from the pole.     
E) The graph of the polar equation consists of all points that are two units from the pole.     
A) The graph of the polar equation consists of all points that are two units from the pole.     
B) The graph of the polar equation consists of all points that are two units from the pole.     
C) The graph of the polar equation consists of all points that are two units from the pole.     
D) The graph of the polar equation consists of all points that are two units from the pole.     
E) The graph of the polar equation consists of all points that are two units from the pole.

Question 12

Find a set of parametric equations for the rectangular equation. ​     ​

Accepted Answer

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

Question 13

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 14

In a suspension bridge, the shape of the suspension cables is parabolic.The bridge shown in the figure has towers that are 1000 m apart, and the lowest point of the suspension cables is 200 m below the top of the towers.Find the equation of the parabolic part of the cables, placing the origin of the coordinate system at the lowest point of the cable. ​
NOTE: This equation is used to find the length of the cable needed in the construction of the bridge.
​   ​

Accepted Answer

A) x 2 = 2,500y 
B) y 2 = 5,000x 
C) x 2 = 1,250y 
D) x 2 = 5,000y 
E) x 2 = -1,250y 
A) x 2 = 2,500y 
B) y 2 = 5,000x 
C) x 2 = 1,250y 
D) x 2 = 5,000y 
E) x 2 = -1,250y

Question 15

Find the angle   (in radians and degrees) between the lines.Round your answer to four decimal places for radians and round your answer to one decimal places for degree. ​   ​

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 and center at the origin. ​
Vertices: (0,±3); focies: (0,±7)
​ ​

Accepted Answer

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

Question 17

Convert the polar equation to rectangular form. ​   ​

Accepted Answer

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

Question 18

The Falls Incline Railway in Niagara Falls, Ontario, Canada is an inclined railway that was designed to carry people from the City of Niagara Falls to Queen Victoria Park.The railway is approximately 130 feet long with a 46% uphill grade (see figure).Find the inclination   of the railway.Round your answer to four decimal places for radians and round your answer to one decimal places for degree. ​   ​   ​

Accepted Answer

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

Question 19

Graph the hyperbola. ​   ​

Accepted Answer

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

Question 20

Find the center and foci of the hyperbola.

Accepted Answer

A) center: (-5, 8), foci: (-11, 8), (1, 8) 
B) center: (-5, 8), foci: (-5, 2), (-5, 14) 
C) center: (-8, 5), foci: (-8, -1), (-8, 11) 
D) center: (8, -5), foci: (2, -5), (14, -5) 
E) center: (5, -8), foci: (5, -14), (5, -2) 
A) center: (-5, 8), foci: (-11, 8), (1, 8) 
B) center: (-5, 8), foci: (-5, 2), (-5, 14) 
C) center: (-8, 5), foci: (-8, -1), (-8, 11) 
D) center: (8, -5), foci: (2, -5), (14, -5) 
E) center: (5, -8), foci: (5, -14), (5, -2)

Find the standard form of the equation of the hyperbola with the given characteristics and center at the origin. Vertices: ; asymptotes:

Use the Quadratic Formula to solve for .

Find the center, vertices and foci of the hyperbola.

Select the correct graph of the polar equation.Describe your viewing window.

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

Select the parametric equations matching with the following graph.

Select the correct graph of the polar equation.Describe your viewing window.

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

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

Find the center and foci of the ellipse.

Describe the graph of the polar equation and find the corresponding rectangular equation.Select the correct graph.

Find a set of parametric equations for the rectangular equation.

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

Find the angle (in radians and degrees) between the lines.Round your answer to four decimal places for radians and round your answer to one decimal places for degree.

Find the standard form of the equation of the hyperbola with the given characteristics and center at the origin. Vertices: (0,±3); focies: (0,±7)

Convert the polar equation to rectangular form.

Graph the hyperbola.

Find the center and foci 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 hyperbola with the given characteristics and center at the origin. ​ Vertices: ; asymptotes: ​

Use the Quadratic Formula to solve for . ​ ​

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

Select the correct graph of the polar equation.Describe your viewing window. ​ ​

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

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

Select the correct graph of the polar equation.Describe your viewing window. ​ ​

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

Find the standard form of the equation of the parabola with the given characteristic(s) and vertex at the origin. ​ Focus: (0, ) ​

Find the center and foci of the ellipse. ​ ​

Describe the graph of the polar equation and find the corresponding rectangular equation.Select the correct graph. ​ ​

Find a set of parametric equations for the rectangular equation. ​ ​

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

Find the angle (in radians and degrees) between the lines.Round your answer to four decimal places for radians and round your answer to one decimal places for degree. ​ ​

Find the standard form of the equation of the hyperbola with the given characteristics and center at the origin. ​ Vertices: (0,±3); focies: (0,±7) ​ ​

Convert the polar equation to rectangular form. ​ ​

Graph the hyperbola. ​ ​

Find the center and foci of the hyperbola.

Trigonometry

Analytic-Trigonometry

Additional-Topics-In-Trigonometry

Complex-Numbers

Exponential-And-Logarithmic-Functions

Prerequisites

Filters

Find the standard form of the equation of the hyperbola with the given characteristics and center at the origin. Vertices: ; asymptotes:

Use the Quadratic Formula to solve for .

Find the center, vertices and foci of the hyperbola.

Select the correct graph of the polar equation.Describe your viewing window.

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

Select the parametric equations matching with the following graph.

Select the correct graph of the polar equation.Describe your viewing window.

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

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

Find the center and foci of the ellipse.

Describe the graph of the polar equation and find the corresponding rectangular equation.Select the correct graph.

Find a set of parametric equations for the rectangular equation.

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

Find the angle (in radians and degrees) between the lines.Round your answer to four decimal places for radians and round your answer to one decimal places for degree.

Find the standard form of the equation of the hyperbola with the given characteristics and center at the origin. Vertices: (0,±3); focies: (0,±7)

Convert the polar equation to rectangular form.

Graph the hyperbola.