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NDA 2024 · PYQ · Application of Integration / Area · medium

The circle x² + y² - 2x = 0 is divided into two parts by the line y = x. Let A₁ and A₂ respectively be the areas of the major and minor parts. What is the value of 2(A₁ + A₂)/(A₁ - 3A₂)?

Answer

The correct answer is A: π. A₁ + A₂ = total area = π. A₁ = (3π + 2)/4, A₂ = (π - 2)/4.

  1. A.π✓ Correct
  2. B.1
  3. C.-1
  4. D.-π

Explanation

A₁ + A₂ = total area = π. A₁ = (3π + 2)/4, A₂ = (π - 2)/4. A₁ - 3A₂ = (3π + 2)/4 - 3(π - 2)/4 = (3π + 2 - 3π + 6)/4 = 8/4 = 2. So 2(A₁ + A₂)/(A₁ - 3A₂) = 2π/2 = π.
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