2025 NYJC Promo Q1

A curve is defined by the parametric equations

1. Show that the equation of the tangent to the curve at the point \(P(2p^2+5,4p^3-2)\) is \(y=3px-2p^3-15p-2\).[2]
2. Show algebraically that there is exactly one point on the curve at which the tangent passes through the point \((3,26)\).[3]