For real number 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 and Area (x, y) : x^ 2 + y^ 2 b^ 2 and x^ 2 /a^ 2 + y^ 2 /b^ 2 1 = 18 . Then the value of (a - b)^ 2 is equal to _____.

JEE Main 2022 Mathematics question

For real number a, b (a > b > 0), let Area{(x, y) : and 1} = and Area{(x, y) : and 1} = . Then the value of is equal to .

Answer: 12

Solution

The first region is the part of the circle of radius a lying outside the ellipse, with area , so a(a − b) = 30. The second is the part of the ellipse outside the circle of radius b, with

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Question ID VK-035250