Solar Cooker, Anyone?

Let ${{y}^{2}}=2px$ , $AB$ , $AD$ and $F$ be the equation , the diameter, the axis of symmetry and the focus of the of the parabola respectively.
Then $OA=5$ is the distance between the bottom, $O$ , of the solar cooker to the edge of the cooker.

By Pythagorean theorem on the right-angled $\triangle OAD$ , $OD=4$ , hence the point $A$ has coordinates $\left( 4,3 \right)$ . These coordinates satisfy the equation of the parabola, thus ${{3}^{2}}=2p\times 4\Rightarrow p=\dfrac{9}{8}$ . The point where the cooking temperature is maximum is the focus of the parabola, whose coordinates are $\left( \dfrac{p}{2},\ 0 \right)\equiv \left( \dfrac{9}{16},\ 0 \right)$ , hence, the required height from the bottom of the bowl is $\dfrac{9}{16}$ .

For the answer, $a+b=\boxed{25}$ .