Question

Let ‘O’ be the centre of ellipse for which A,B are end points of major axis and C,D are end points of minor axis, F is focus of the ellipse. If in radius of $\Delta OCF$ is '1' then $|AB|\times |CD|=$

• A. 65
• B. 52
• C. 78
• D. 47

Answer 1

The correct option is A 65

$r=\frac{\Delta }{S}\Rightarrow \Delta =S\frac{1}{2}\left(ae\right)b=\frac{ae+b+\sqrt{a^2{e}^2+b^2}}{2}ae=6\Rightarrow 6b=6+b+\sqrt{36+b^2}\Rightarrow b=\frac{5}{2}\Rightarrow a^2(1-e^2)=\frac{25}{4}\Rightarrow a^2-36=\frac{25}{4}\Rightarrow a=\frac{13}{2}$
Hence $|AB|\times |CD|=$ 2a x 2b =65