For real numbers a, b (a > b > 0), let Area (x,y):x² + y² ≤ a² and (x²)/(a²) + (y²)/(b²) ≥ 1 = 30π and Area (x,y):x² + y² ≤ b² and (x²)/(a²) + (y²)/(b²) ≤ 1 = 18π Then, the value of (a - b)² is equal to _ _ _ _ _ _.

Integral Calculus: JEE Main 2022 Mathematics question

JEE Main 2022 · 29 Jun, Evening shift · Q26

JEE Main 202229 Jun, Evening shiftMathematicsHardIntegral Calculus369× since 2002

For real numbers a, b (a > b > 0), let Area

\left\{ {(x,y):{x^2} + {y^2} \le {a^2}\,and\,{{{x^2}} \over {{a^2}}} + {{{y^2}} \over {{b^2}}} \ge 1} \right\} = 30\pi

and Area

\left\{ {(x,y):{x^2} + {y^2} \le {b^2}\,and\,{{{x^2}} \over {{a^2}}} + {{{y^2}} \over {{b^2}}} \le 1} \right\} = 18\pi

Then, the value of (a

-

b)² is equal to ___________.

Your answerType your answer. Integers and decimals are accepted.

JEE Main 2022 Integral Calculus Question with Answer (29 Jun Evening shift, Q26) | JEE Arc