Question

If maximum distance of any point on the curve $5x^2+4y^2$ $+xy-2=0$ from its centre be $L$ and $L=\frac{a}{\sqrt{b-\sqrt{2}}}$, then $(b-a)$ is

Answer 1

Answer: 7

Centre $(0,0)$.
Let $P(r\cos \theta ,r\sin \theta )$ be any point on ellipse
$\Rightarrow r^2=\frac{4}{9+\cos 2\theta +\sin 2\theta }$
$r_{\max }=\frac{2}{\sqrt{9-\sqrt{2}}}$