Find the slope of the normal to the curve `x=a\ cos^3theta` , `y=a\ s in^3theta` at `theta=pi/4` .

Answer

Slope of normal at `theta=pi/4` `=1`

Explanation

Given,
$$ x=a \cos ^{3} \theta, y=a \sin ^{3} \theta $$
$$
\begin{aligned}
&\frac{\mathrm{dx}}{\mathrm{d} \theta}=-3 \mathrm{a} \cos ^{2} \theta \sin \theta \\
&\frac{\mathrm{dy}}{\mathrm{d} \theta}=3 \mathrm{a} \sin ^{2} \theta \cos \theta
...