Area of the greatest rectangle that can be inscribed in the
ellipse \[{{{x^2}} \over {{a^2}}} + {{{y^2}} \over {{b^2}}} = 1\]
Solutions · 1
Official solution
Area of rectangle ABCD \[ = 2a\,\cos \,\theta \]
\[\left( {2b\,\sin \,\theta } \right) = 2ab\,\sin \,2\theta \]
\[ \Rightarrow \] Area of greatest rectangle is equal to 2ab
When \[\sin \,2\theta = 1.\]