# An engineer is designing a flashlight using a parabolic

**Chapter 13, Problem 13.1.320**

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An engineer is designing a flashlight using a parabolic reflecting mirror and a light source, as shown. The casting has a diameter of 4 inches and a depth of 2 inches. The parabola is positioned in a rectangular coordinate system with its vertex at the origin. 4 inches 2 inches y x (2, 2) a. Write an equation in the form y ax2 for the parabola used to shape the mirror. b. The light source should be placed at the focus (0, p). The value of p is given by the equation a 1 4p . Where should the light source be placed relative to the mirrors vertex?

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