Question 1

Find the vertices, foci, and asymptotes for the hyperbola given by the equation.

Accepted Answer

A) vertices:   , foci:   , asymptotes:   
B) vertices:   , foci:   , asymptotes:   
C) vertices:   , foci:   , asymptotes:   
D) vertices:   foci:   , asymptotes:   
E) vertices:   , foci:   , asymptotes:   
A) vertices:   , foci:   , asymptotes:   
B) vertices:   , foci:   , asymptotes:   
C) vertices:   , foci:   , asymptotes:   
D) vertices:   foci:   , asymptotes:   
E) vertices:   , foci:   , asymptotes:

Question 2

Find the center, vertices, and foci of the ellipse given by the equation.

Accepted Answer

A) center:   , vertices:   , foci:   
B) center:   , vertices:   , foci:   
C) center:   , vertices:   , foci:   
D) center:   , vertices:   , foci:   
E) center:   , vertices:   , foci:   
A) center:   , vertices:   , foci:   
B) center:   , vertices:   , foci:   
C) center:   , vertices:   , foci:   
D) center:   , vertices:   , foci:   
E) center:   , vertices:   , foci:

Question 3

Graph the equation.

Accepted Answer

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

Question 4

Find the equation in standard form of the parabola with vertex at   and focus   .

Accepted Answer

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

Question 5

Sketch the graph of the polar equation.

Accepted Answer

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

Question 6

Graph the equation.

Accepted Answer

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

Question 7

Find the vertices and foci of the ellipse given by the equation.

Accepted Answer

A) vertices:   , foci:   
B) vertices:   , foci:   
C) vertices:   , foci:   
D) vertices:   , foci:   
E) vertices:   , foci:   
A) vertices:   , foci:   
B) vertices:   , foci:   
C) vertices:   , foci:   
D) vertices:   , foci:   
E) vertices:   , foci:

Question 8

Use the eccentricity to find the equation of the hyperbola in standard form. eccentricity 2, foci (12, 0)and ( - 12, 0)

Accepted Answer

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

Question 9

Find the vertices and foci of the ellipse given by the equation.

Accepted Answer

A) vertices:   
B) vertices:   
C) vertices:   
D) vertices:   
E) vertices:   
A) vertices:   
B) vertices:   
C) vertices:   
D) vertices:   
E) vertices:

Question 10

Find the vertex, focus, and directrix of the parabola given by the equation.

Accepted Answer

A) vertex: (0, -3), focus: (0, 0), directrix: y = 3 
B) vertex: (0, 0), focus: (0, 3), directrix: y = -3 
C) vertex: (0, 0), focus: (0, -3), directrix: y = 3 
D) vertex: (0, 0), focus: (0, -12), directrix: y = 12 
E) vertex: (0, -3), focus: (0, 3), directrix: y = 0 
A) vertex: (0, -3), focus: (0, 0), directrix: y = 3 
B) vertex: (0, 0), focus: (0, 3), directrix: y = -3 
C) vertex: (0, 0), focus: (0, -3), directrix: y = 3 
D) vertex: (0, 0), focus: (0, -12), directrix: y = 12 
E) vertex: (0, -3), focus: (0, 3), directrix: y = 0

Question 11

Find a polar form of the equation   .

Accepted Answer

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

Question 12

The parabolic mirror in a certain telescope has a diameter of 112 inches and a concave depth of 3.69985 inches. Determine the location of its focus above the vertex. Round to the nearest inch.

Accepted Answer

A) 159 inches 
B) 212 inches 
C) 583 inches 
D) 477 inches 
E) 265 inches 
A) 159 inches 
B) 212 inches 
C) 583 inches 
D) 477 inches 
E) 265 inches

Question 13

A vertical cross section of a cooling tower is a portion of a hyperbola, as shown in the diagram below. The standard form of the equation of the hyperbolic cross section is   where x and y are measured in feet. The horizontal cross sections of the tower are circles.   Find the radius of the top of the tower. Round to the nearest foot.

Accepted Answer

A) 90 feet 
B) 88 feet 
C) 93 feet 
D) 87 feet 
E) 85 feet 
A) 90 feet 
B) 88 feet 
C) 93 feet 
D) 87 feet 
E) 85 feet

Question 14

Sketch the graph of the polar equation.

Accepted Answer

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

Question 15

Use the eccentricity to find the equation of the hyperbola in standard form. center ( - 2, - 6), conjugate axis of length 8 with the transverse axis parallel to the x -axis, eccentricity 3

Accepted Answer

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

Question 16

Find the equation in standard form of the ellipse with center (8, 5), minor axis parallel to the x -axis and of length 6, and that passes through point (9.5, 11).

Accepted Answer

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

Question 17

An architect wishes to design a large room that will be a whispering gallery. The ceiling of the room has a cross section that is an ellipse with a major axis measuring 286 feet and a minor axis measuring 90 feet. Assume the center is at (0, 0)and the major axis lies on the x -axis. How far to the right and left of center are the foci located? Approximate the answer to the nearest tenth of a foot.

Accepted Answer

A) 135.7 ft 
B) 271.5 ft 
C) 45.0 ft 
D) 143.0 ft 
E) 196.0 ft 
A) 135.7 ft 
B) 271.5 ft 
C) 45.0 ft 
D) 143.0 ft 
E) 196.0 ft

Question 18

Use the quadratic formula to solve for y in terms of x . Then use a graphing utility to graph the equation.

Accepted Answer

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

Question 19

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

Accepted Answer

A) Ellipse 
B) Hyperbola 
C) Parabola 
A) Ellipse 
B) Hyperbola 
C) Parabola

Question 20

Graph the equation.

Accepted Answer

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

Find the vertices, foci, and asymptotes for the hyperbola given by the equation.

Find the center, vertices, and foci of the ellipse given by the equation.

Graph the equation.

Find the equation in standard form of the parabola with vertex at and focus .

Sketch the graph of the polar equation.

Graph the equation.

Find the vertices and foci of the ellipse given by the equation.

Use the eccentricity to find the equation of the hyperbola in standard form. eccentricity 2, foci (12, 0)and ( - 12, 0)

Find the vertices and foci of the ellipse given by the equation.

Find the vertex, focus, and directrix of the parabola given by the equation.

Find a polar form of the equation .

The parabolic mirror in a certain telescope has a diameter of 112 inches and a concave depth of 3.69985 inches. Determine the location of its focus above the vertex. Round to the nearest inch.

Sketch the graph of the polar equation.

Use the eccentricity to find the equation of the hyperbola in standard form. center ( - 2, - 6), conjugate axis of length 8 with the transverse axis parallel to the x -axis, eccentricity 3

Find the equation in standard form of the ellipse with center (8, 5), minor axis parallel to the x -axis and of length 6, and that passes through point (9.5, 11).

Use the quadratic formula to solve for y in terms of x . Then use a graphing utility to graph the equation.

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

Graph the equation.

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Exam 8: Topics in Analytic Geometry

Find the vertices, foci, and asymptotes for the hyperbola given by the equation.

Find the center, vertices, and foci of the ellipse given by the equation.

Graph the equation.

Find the equation in standard form of the parabola with vertex at and focus .

Sketch the graph of the polar equation.

Graph the equation.

Find the vertices and foci of the ellipse given by the equation.

Use the eccentricity to find the equation of the hyperbola in standard form. eccentricity 2, foci (12, 0)and ( - 12, 0)

Find the vertices and foci of the ellipse given by the equation.

Find the vertex, focus, and directrix of the parabola given by the equation.

Find a polar form of the equation .

The parabolic mirror in a certain telescope has a diameter of 112 inches and a concave depth of 3.69985 inches. Determine the location of its focus above the vertex. Round to the nearest inch.

Sketch the graph of the polar equation.

Use the eccentricity to find the equation of the hyperbola in standard form. center ( - 2, - 6), conjugate axis of length 8 with the transverse axis parallel to the x -axis, eccentricity 3

Find the equation in standard form of the ellipse with center (8, 5), minor axis parallel to the x -axis and of length 6, and that passes through point (9.5, 11).

Use the quadratic formula to solve for y in terms of x . Then use a graphing utility to graph the equation.

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

Graph the equation.

Equations and Inequalities

Functions and Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions

Trigonometric Identities and Equations

Applications of Trigonometry

Systems of Equations and Inequalities

Matrices

Sequences, Series, and Probability

Preliminary Concepts

Filters