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MHT CET202619 April 2026Evening ShiftMathematicsArea Under CurvesActual

The area (in square units) of the region bounded by the circle x^2 + y^2 = 9 and the parabola y^2 8x is...

Options

  1. A8 2 3 + 9 2 - 2 2 - 9 ⁻¹ 1 3
  2. B8 2 3 + 9 2 + 2 2 + 9 ⁻¹ 1 3
  3. C4 2 3 + 9 4 - 2 - 9 2 ⁻¹ 1 3
  4. D4 2 3 + 9 4 + 2 + 9 2 ⁻¹ 1 3

Correct answer

A. 8 2 3 + 9 2 - 2 2 - 9 ⁻¹ 1 3

Step-by-step solution

To find the points of intersection of the circle x^2 + y^2 = 9 and the parabola y^2 = 8x , substitute y^2 = 8x into the equation of the circle: x^2 + 8x - 9 = 0 (x + 9)(x - 1) = 0 Since x 0 for the parabola, we get x = 1 . The required region is bounded by x^2 + y^2 9 and y^2 8x . This region is symmetric with respect to the x-axis. The total area A is given by: A = 2 ( ₀¹ 8x , dx + ₁³ 9 - x^2 , dx ) Evaluating the first integral: ₀¹ 8x , dx = 2 2 [ 2 3 x^ 3/2 ]₀¹ = 4 2 3 Evaluating the second integral: ₁³ 9 - x^2

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