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For parts a and b, Figure 12-7c shows an ellipse of eccentricity 0.8, with foci at the

Precalculus with Trigonometry: Concepts and Applications | 1st Edition | ISBN: 9781559533911 | Authors: Foerster ISBN: 9781559533911 468

Solution for problem R.4 Chapter 12-7

Precalculus with Trigonometry: Concepts and Applications | 1st Edition

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Precalculus with Trigonometry: Concepts and Applications | 1st Edition | ISBN: 9781559533911 | Authors: Foerster

Precalculus with Trigonometry: Concepts and Applications | 1st Edition

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Problem R.4

For parts a and b, Figure 12-7c shows an ellipse of eccentricity 0.8, with foci at the points (6.4, 0) and (6.4, 0) and one directrix at x = 10. The point shown on the ellipse has x = 3. Figure 12-7c a. Measure the three distances d1, d2, and d3 using the scales shown. Confirm that d2 = ed1. Confirm that d2 + d3 = 16, the major diameter. b. Write a Cartesian equation for the ellipse. Use the equation to calculate y for the point where x = 3. Use the value of y and the Pythagorean theorem to calculate d2 and d3 exactly. Do your measurements in part a agree with the calculated values? Does d2 + d3 equal 16 exactly? c. Billiards Table Problem: An elliptical billiards table is to be built with eccentricity 0.9 and foci at the points (0, 81) and (0, 81), where x and y are in centimeters. Find the major and minor radii. Write parametric equations for the ellipse, plot them on your grapher, and sketch the result. If a ball at one focus is hit in any direction and bounces at the edge of the table, through what special point will the path of the ball go? d. Identify the conic section whose equation is shown here. Sketch the graph. Find the four radii and the eccentricity. e. A parabola has directrix x = 4 and focus at point (0, 0). Sketch this information. Find the particular Cartesian equation. Plot the graph and sketch it on your paper. f. Find the parametric equations of the hyperbola with eccentricity and foci at points (2, 1) and (2, 7). Plot the graph and sketch the result.

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Chapter 12-7, Problem R.4 is Solved
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Textbook: Precalculus with Trigonometry: Concepts and Applications
Edition: 1
Author: Foerster
ISBN: 9781559533911

The answer to “For parts a and b, Figure 12-7c shows an ellipse of eccentricity 0.8, with foci at the points (6.4, 0) and (6.4, 0) and one directrix at x = 10. The point shown on the ellipse has x = 3. Figure 12-7c a. Measure the three distances d1, d2, and d3 using the scales shown. Confirm that d2 = ed1. Confirm that d2 + d3 = 16, the major diameter. b. Write a Cartesian equation for the ellipse. Use the equation to calculate y for the point where x = 3. Use the value of y and the Pythagorean theorem to calculate d2 and d3 exactly. Do your measurements in part a agree with the calculated values? Does d2 + d3 equal 16 exactly? c. Billiards Table Problem: An elliptical billiards table is to be built with eccentricity 0.9 and foci at the points (0, 81) and (0, 81), where x and y are in centimeters. Find the major and minor radii. Write parametric equations for the ellipse, plot them on your grapher, and sketch the result. If a ball at one focus is hit in any direction and bounces at the edge of the table, through what special point will the path of the ball go? d. Identify the conic section whose equation is shown here. Sketch the graph. Find the four radii and the eccentricity. e. A parabola has directrix x = 4 and focus at point (0, 0). Sketch this information. Find the particular Cartesian equation. Plot the graph and sketch it on your paper. f. Find the parametric equations of the hyperbola with eccentricity and foci at points (2, 1) and (2, 7). Plot the graph and sketch the result.” is broken down into a number of easy to follow steps, and 284 words. This full solution covers the following key subjects: . This expansive textbook survival guide covers 106 chapters, and 2321 solutions. This textbook survival guide was created for the textbook: Precalculus with Trigonometry: Concepts and Applications, edition: 1. The full step-by-step solution to problem: R.4 from chapter: 12-7 was answered by , our top Calculus solution expert on 03/16/18, 04:16PM. Precalculus with Trigonometry: Concepts and Applications was written by and is associated to the ISBN: 9781559533911. Since the solution to R.4 from 12-7 chapter was answered, more than 235 students have viewed the full step-by-step answer.

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For parts a and b, Figure 12-7c shows an ellipse of eccentricity 0.8, with foci at the