For a curve, the parametric equations are $x = a\cos^4 t$ and $y = a\sin^4 t$, with $a$ a positive constant.
(i)[3]
Express $\frac{dy}{dx}$ as a function of $t$.
(ii)[3]
Show that the tangent to the curve at the point with parameter $t$ has equation $x\sin^2 t + y\cos^2 t = a\sin^2 t\cos^2 t$.
(iii)[2]
Hence show that, if the tangent meets the $x$-axis at $P$ and the $y$-axis at $Q$, then $OP + OQ = a$, where $O$ is the origin.
Worked solution & mark scheme
This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “State $\frac{dx}{dt}=-4a\cos^3 t\sin t$, or $\frac{dy}{dt}=4a\sin^3 t\cos t$” …