# Cool Parabola

Geometry Level 4

A normal is drawn to the parabola $${ y }^{ 2 }=9x$$ at the point. $$P(4,6)$$. A circle is described on $$SP$$ as diameter; where $$S$$ is the focus. The length of the intercept made by the circle on the normal at point $$P$$ can be expressed in the form of $$\frac { a }{ b }$$ where $$a$$ and $$b$$ are co-prime. Find $$a+b$$.

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