Solar Cooker, Anyone?

Geometry Level 4

Jimmy wants to build a parabolic solar cooker for his culinary project. It is 6 meters in diameter and the distance between the bottom of his solar cooker to the edge of the cooker is 5 meters.

At what height from the bottom of the bowl should he put his food in order to maximize the cooking temperature?

If the height, in meters, is expressible in the form \(\dfrac{a}{b}\), where \(a\) and \(b\) are coprime positive integers, find \(a+b\).

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