Draw a rectangle whose two sides are tangent to the ellipse and the other two are normal to the ellipse.

Now how to find the area enclosed by the locus of the vertex of the rectangle at which the normals meet.

Answer:-

We are required to find the locus of the point (h,k) from which two mutually perpendicular lines can be drawn that are normal to the ellipse.

Normal to the ellipse at the point $(a *\cos{\theta},b*\sin{\theta})$ is given by $a*x\sec{\theta}- b*y\csc{\theta}=a^2-b^2$ and slope of this normal is given by $m=\frac{a}{b} \tan{\theta}$

Now how to proceed further?

Note:- Graphical visualisation is appreciated.