Explanation Given: About hyperbolic mirrors: Hyperbolas have interesting reflective properties that make them useful for lenses and mirrors. For example, if a ray of light strikes a convex hyperbolic mirror on a line that would (theoretically) pass through its rear focus, it is reflected through the front focus. This property, and that of the parabola, were used to develop the Cassegrain telescope in 1672. The focus of the parabolic mirror and the rear focus of the hyperbolic mirror are the same point. The rays are collected by the parabolic mirror, then are reflected toward the (common) focus, and thus are reflected by the hyperbolic mirror through the opening to its front focus, where the eyepiece is located. The equation of the hyperbola is y 2 9 − x 2 16 = 1 and the focal length (distance from the vertex to the focus) of the parabola is 6. Formula used: Equation of the parabola is x 2 = 4 a ( y − k ) . Calculation: Let us assume that the center of hyperbola is origin. From the given equation we see that the transverse axis is parallel to y -axis . Let the foci of the hyperbola be ( 0 , ± c ) . c 2 = a 2 + b 2 = 9 + 16 = 25 or c = 5 Therefore, foci of the hyperbola are at ( 0 , ± 5 ) ...

Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (4th Edition)

4th Edition

ISBN: 9780134686974

Author: Michael Sullivan, Michael Sullivan III

Publisher: PEARSON

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Chapter 9.4, Problem 80AYU

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To find: The equation of the parabola if details of hyperbola are given.

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Chapter 9.4, Problem 79AYU

Chapter 9.4, Problem 81AYU

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Chapter 9 Solutions

Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (4th Edition)

Ch. 9.2 - The formula for the distance d from P 1 =( x 1 , y...Ch. 9.2 - To complete the square of x 2 4x , add_______...Ch. 9.2 - Use the Square Root Method to find the real...Ch. 9.2 - The point that is symmetric with respect to the...Ch. 9.2 - To graph , shift the graph of to the...Ch. 9.2 - A(n)_______ is the collection of all point in a...Ch. 9.2 - True or false The line through the focus and...Ch. 9.2 - For the parabola , the line segment joining the...Ch. 9.2 - Answer Problems 9-12 using the figure. If , the...Ch. 9.2 - Answer Problems 9-12 using the figure. The...

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The equation of the parabola if details of hyperbola are given.

Solution Summary: The author explains that hyperbolas have interesting reflective properties that make them useful for lenses and mirrors.

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To find: The equation of the parabola if details of hyperbola are given.

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Chapter 9 Solutions