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Q.
If maximum distance of any point on the curve $5 x^{2}+4 y^{2}$ $+x y-2=0$ from its centre be $L$ and $L=\frac{a}{\sqrt{b-\sqrt{2}}}$, then $(b-a)$ is
Conic Sections
Solution:
Centre $(0,0)$.
Let $P(r \cos \theta, r \sin \theta)$ be any point on ellipse
$\Rightarrow r^{2}=\frac{4}{9+\cos 2 \theta+\sin 2 \theta}$
$r_{\max }=\frac{2}{\sqrt{9-\sqrt{2}}}$