Let `C` be a curve defined parametrically as `x=a\ cos^3theta` , `y=a\ sin^3theta,\ \ 0lt=thetalt=pi/2` . Determine a point `P` on `C` , where the tangent to `C` is parallel to the chord joining the points `(a ,\ 0)` and `(0,\ a)` .

Answer

Point `P` is `(frac{a}{2 sqrt{2}}, frac{a}{2 sqrt{2}})`

Explanation

let point be `p(x, y)`
Given equation
$$ \begin{aligned} &x=a \cos ^{3} \theta \\ &y=a \sin ^{3} \theta \end{aligned} $$
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