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Conic Sections: JEE Mains 2022 June 29 Shift 2

Hard· Ellipse· +4 / 0
For real numbers a,ba,b (a>b>0)(a>b>0), let
Area{(x,y):x2+y2≤a2 and x2a2+y2b2≥1}=30π\text{Area}\left\{(x,y):x^2+y^2\le a^2\ \text{and}\ \frac{x^2}{a^2}+\frac{y^2}{b^2}\ge1\right\}=30\pi
and
Area{(x,y):x2+y2≥b2 and x2a2+y2b2≤1}=18π\text{Area}\left\{(x,y):x^2+y^2\ge b^2\ \text{and}\ \frac{x^2}{a^2}+\frac{y^2}{b^2}\le1\right\}=18\pi
Then the value of (a−b)2(a-b)^2 is equal to ______.
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