1. A lamp with a parabolic reflector is shown in the figure. The bulb is placed at the focus and the focal diameter is 10 cm. (Assume the vertex O is at the origin. Let the x-axis be horizontal and the y-axis be vertical.) 5 cm 27 cm 5 cm В •D a. Find an equation of the parabola. Explain your reasoning. b. Find the diameter d(C, D) of the opening, 27 cm from the vertex. (Round your answer to the nearest whole number.)

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Q: 9x? + 4y2. - 18х + 16у — 113D0

A: For the detailed solution of the problem follow the next steps.

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Maximization

Have you ever seen a bridge in the shape of a parabola? Where is its maximum on the bridge? The maximum of that bridge is the highest point on that bridge. The process of finding the maximum of the bridge here is called the maximization.