RI Differentiation Tutorial Q11

The parametric equations of a curve are \(x=at\), \(y=a{{t}^{2}}\) where \(a\) is a positive constant. The points \(P\left( ap,\,\,a{{p}^{2}} \right)\) and \(Q\left( aq,\,\,a{{q}^{2}} \right)\) lie on the curve. Find, and simplify an expression, in terms of \(p\) and \(q\), for the gradient of the chord \(PQ\). Deduce, from this expression, the gradient of the curve at the point \(Q\).