A flashlight has a parabolic reflector that reflects light waves from a bulb loc

Question

A flashlight has a parabolic reflector that reflects light waves from a bulb located at the focus. The figure shows a vertical cross section of such a parabolic reflector with the bulb at the focus. Suppose the bulb is 0.4 inch from the vertex of the reflector, and the distance across the widest part of the reflector is 10 inches. Suppose also that the parabola formed by the cross section is located on a grid (The figure may not be drawn to scale.) so that the vertex is at (0, 0). The equation for the parabola is

Explanation / Answer

We know that if a parabola has a horizontal axis, the equation of the parabola is (y - k)2 = 4p(x - h) , where p 0 .Here, the distance between the vertex and the focus of the parabola is 0.4 inch. The vertex is (0, 0). The absolute value of p is the distance between the vertex and the focus. Hence I p I = 0.4 inch. Since the focus is to the right of the vertex, p = 0.4 inch. Hence the equation of the parabola is (y – 0)2 = 4*0.4 ( x – 0) or, y2 = 1.6x

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