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Mathematics · 2022

JEE Main · 29 June 2022, Shift 2 · Q25

For real numbers a, b(a>b>0), let Area {(x, y): x^2+y^2 ≤ a^2. and.x^2/a^2+y^2/b^2 ≥ 1}=30 π and Area {(x, y): x^2+y^2 ≥ b^2. and.x^2/a^2+y^2/b^2 ≤…

For real numbers $\displaystyle a, b(a>b>0)$, let Area $\displaystyle \left\{(x, y): x^2+y^2 \leq a^2\right.$ and $\displaystyle \left.\frac{x^2}{a^2}+\frac{y^2}{b^2} \geq 1\right\}=30 \pi$ and Area $\displaystyle \left\{(x, y): x^2+y^2 \geq b^2\right.$ and $\displaystyle \left.\frac{x^2}{a^2}+\frac{y^2}{b^2} \leq 1\right\}=18 \pi$ Then the value of $\displaystyle (a-b)^2$ is equal to \_\_\_\_.
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JEE Main 2022 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.