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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