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Manipal MET2015MathematicsArea Under Curves

The area of the region bounded by the parabola (y-2)^2=(x-1) , the tangent to the parabola at the point (2,3) and the X -axis, is

Options

  1. A3
  2. B6
  3. C9
  4. D12

Correct answer

C. 9

Step-by-step solution

Given equation of parabola is y^2-4 y-x+5=0 Then, the equation of tangent at (2,3) is 3 y-2(y+3)- (x+2) 2 +5=0 2 y-x-4=0 Required area is given by aligned A & = ₀^3 (x₂-x₁ ) d y & = ₀^3 [ (y-2)^2+1 - 2 y-4 ] d y & = ₀^3 (y^2-6 y+9 ) d y= ₀^3(3-y)^2 d y & =- [ (3-y)^3 3 ]₀^3 aligned A=9

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