imo class 12 application of integrals

The total area of the ellipse x²/a² + y²/b² = 1 is equivalent to the area of a circle with a specific radius R. What is R in terms of a and b?

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The total area of the ellipse x²/a² + y²/b² = 1 is equivalent to the area of a circle with a specific radius R. What is R in terms of a and b?

  • A. √(ab)
  • B. a + b
  • C. (a+b)/2
  • D. ab

Answer: A) √(ab)

Explanation: Area of ellipse = πab. Area of circle = πR². Equating them gives πR² = πab, so R = √(ab).

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