The parametric equations of a curve are $x=at$, $y=a{{t}^{2}}$ where $a$ is a positive constant. The

Question

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 $Q$.

Accepted Answer

$2q$

RI Differentiation Tutorial Q11

RI Differentiation Tutorial Q11

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