# A Normal Problem!

Geometry Level pending

Let the normal at the point $$P$$ to the hyperbola $$\dfrac{(x-2)^2}{10} - \dfrac{(y+4)^2}{28} = 1$$ meet the tranverse axis in $$A$$ and the conjugate axis in $$B$$. A perpendicular $$CF$$ is drawn from the centre of the hyperbola to the normal. If $$p=PA \times PF$$ and $$q = PF \times PB$$, find the value of $$p+q$$.

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