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Exam 8: Topics in Analytic Geometry

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Exam 1: Equations and Inequalities67 Questionsadd course
Exam 2: Functions and Graphs88 Questionsadd course
Exam 3: Polynomial and Rational Functions79 Questionsadd course
Exam 4: Exponential and Logarithmic Functions95 Questionsadd course
Exam 5: Trigonometric Functions58 Questionsadd course
Exam 6: Trigonometric Identities and Equations25 Questionsadd course
Exam 7: Applications of Trigonometry24 Questionsadd course
Exam 8: Topics in Analytic Geometry102 Questionsadd course
Exam 9: Systems of Equations and Inequalities35 Questionsadd course
Exam 10: Matrices29 Questionsadd course
Exam 11: Sequences, Series, and Probability66 Questionsadd course
Exam 12: Preliminary Concepts63 Questionsadd course
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Two radio transmitters are positioned along the coast, 250 miles apart. A signal is sent simultaneously from each transmitter. The signal from transmitter Two radio transmitters are positioned along the coast, 250 miles apart. A signal is sent simultaneously from each transmitter. The signal from transmitter is received by a ship s LORAN 800 microseconds after the ship receives the signal from . The radio signals travel at 0.186 mile per microsecond. Find an equation of a hyperbola, with foci at and on which the ship is located. Round parameters to the nearest hundredth. is received by a ship s LORAN 800 microseconds after the ship receives the signal from Two radio transmitters are positioned along the coast, 250 miles apart. A signal is sent simultaneously from each transmitter. The signal from transmitter is received by a ship s LORAN 800 microseconds after the ship receives the signal from . The radio signals travel at 0.186 mile per microsecond. Find an equation of a hyperbola, with foci at and on which the ship is located. Round parameters to the nearest hundredth. . The radio signals travel at 0.186 mile per microsecond. Two radio transmitters are positioned along the coast, 250 miles apart. A signal is sent simultaneously from each transmitter. The signal from transmitter is received by a ship s LORAN 800 microseconds after the ship receives the signal from . The radio signals travel at 0.186 mile per microsecond. Find an equation of a hyperbola, with foci at and on which the ship is located. Round parameters to the nearest hundredth. Find an equation of a hyperbola, with foci at Two radio transmitters are positioned along the coast, 250 miles apart. A signal is sent simultaneously from each transmitter. The signal from transmitter is received by a ship s LORAN 800 microseconds after the ship receives the signal from . The radio signals travel at 0.186 mile per microsecond. Find an equation of a hyperbola, with foci at and on which the ship is located. Round parameters to the nearest hundredth. and Two radio transmitters are positioned along the coast, 250 miles apart. A signal is sent simultaneously from each transmitter. The signal from transmitter is received by a ship s LORAN 800 microseconds after the ship receives the signal from . The radio signals travel at 0.186 mile per microsecond. Find an equation of a hyperbola, with foci at and on which the ship is located. Round parameters to the nearest hundredth. on which the ship is located. Round parameters to the nearest hundredth.

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Question 21

Sketch the graph of the polar equation. Sketch the graph of the polar equation.

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Question 22

Graph the parametric equation by eliminating the parameter. Graph the parametric equation by eliminating the parameter.

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Question 23

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

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Question 24

Sketch the graph of the polar equation. Sketch the graph of the polar equation.

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Question 25

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

(Multiple Choice)
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Question 26

Use the Conic Identification Theorem to identify the graph of the equation as a parabola, an ellipse, or a hyperbola. Use the Conic Identification Theorem to identify the graph of the equation as a parabola, an ellipse, or a hyperbola.

(Multiple Choice)
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Question 27

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

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Question 28

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

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Question 29

An architect wishes to design a large room 148 feet long that will be a whispering gallery. The ceiling of the room has a cross section that is an ellipse whose foci are to be located 20 feet to the right and the left of center, as shown in the following figure where d is 148 feet and x is 20 feet. An architect wishes to design a large room 148 feet long that will be a whispering gallery. The ceiling of the room has a cross section that is an ellipse whose foci are to be located 20 feet to the right and the left of center, as shown in the following figure where d is 148 feet and x is 20 feet. Find the height h of the elliptical ceiling (to the nearest tenth of a foot). Find the height h of the elliptical ceiling (to the nearest tenth of a foot).

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Question 30

Graph the equation. Graph the equation.

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Question 31

Find the acute angle of rotation a that eliminates the xy term. State approximate solution to the nearest 0.1 . Find the acute angle of rotation a that eliminates the xy term. State approximate solution to the nearest 0.1 .

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Question 32

Find the equation in standard form of a hyperbola with vertices ( 1, 1)and ( 1, 5)and eccentricity Find the equation in standard form of a hyperbola with vertices ( 1, 1)and ( 1, 5)and eccentricity . .

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Question 33

Use the definition of a hyperbola to find the equation of the hyperbola in standard form. foci (7, 0)and ( - 7, 0); passes through the point Use the definition of a hyperbola to find the equation of the hyperbola in standard form. foci (7, 0)and ( - 7, 0); passes through the point

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Question 34

A circular vent pipe with a diameter of 8.5 inches is placed on a roof that has a slope of A circular vent pipe with a diameter of 8.5 inches is placed on a roof that has a slope of as shown in the figure below. The intersection of the vent pipe and the roof is an ellipse. To the nearest hundredth of an inch, what are the lengths of the major and minor axes? as shown in the figure below. A circular vent pipe with a diameter of 8.5 inches is placed on a roof that has a slope of as shown in the figure below. The intersection of the vent pipe and the roof is an ellipse. To the nearest hundredth of an inch, what are the lengths of the major and minor axes? The intersection of the vent pipe and the roof is an ellipse. To the nearest hundredth of an inch, what are the lengths of the major and minor axes?

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Question 35

Graph the parametric equation by plotting several points. Graph the parametric equation by plotting several points.

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Question 36

Sketch the graph of the polar equation. Sketch the graph of the polar equation.

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Question 37

The line segment that has endpoints on a parabola, passes through the focus of the parabola, and is perpendicular to the axis of symmetry is called the latus rectum of the parabola. The line segment that has endpoints on a parabola, passes through the focus of the parabola, and is perpendicular to the axis of symmetry is called the latus rectum of the parabola. Find the length of the latus rectum for the parabola . Find the length of the latus rectum for the parabola The line segment that has endpoints on a parabola, passes through the focus of the parabola, and is perpendicular to the axis of symmetry is called the latus rectum of the parabola. Find the length of the latus rectum for the parabola . .

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Question 38

Find the equation in standard form of an ellipse with eccentricity Find the equation in standard form of an ellipse with eccentricity , center at (0, 0), and major axis on the x -axis and of length 14. , center at (0, 0), and major axis on the x -axis and of length 14.

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Question 39

Plot the point on a polar coordinate system. Plot the point on a polar coordinate system.

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Question 40
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