The tangent at any point on the curve $\mathrm{x}={\mathrm{acos}}^3 \mathrm{\theta },\mathrm{y}={\mathrm{asin}}^{3 }\mathrm{\theta }$ meets the coordinate axes in P and Q. the locus of the mid point of PQ is

Given that $\mathrm{x}={\mathrm{acos}}^3 \mathrm{\theta },\mathrm{y}={\mathrm{asin}}^3 \mathrm{\theta }$
$\begin{array}{r}\text{ equation of }\tan \text{gent at }\mathrm{\theta }\text{ is }\frac{\mathrm{x}}{\mathrm{acos}\mathrm{\theta }}+\frac{\mathrm{y}}{\mathrm{asin}\mathrm{\theta }}=1\\ \therefore \mathrm{P}=(\mathrm{acos}\mathrm{\theta },0)\mathrm{Q}=(0,\mathrm{asin}\mathrm{\theta })\end{array}$
$\text{ locus is }\left({\mathrm{x}}_1,{\mathrm{y}}_1\right)=\left(\frac{\mathrm{acos} \mathrm{\theta }}{2},\frac{\mathrm{asin} \mathrm{\theta }}{2}\right)$
$\begin{array}{r}\Rightarrow \cos \mathrm{\theta }=\frac{2{\mathrm{x}}_1}{\mathrm{a}},\sin \mathrm{\theta }=\frac{2{\mathrm{y}}_1}{\mathrm{a}}\\ \text{ elinating }\mathrm{\theta }\Rightarrow 4\left({\mathrm{x}}^2+{\mathrm{y}}^2\right)={\mathrm{a}}^2\end{array}$