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MHT CET202123 Sep 2021Evening ShiftMathematicsArea Under CurvesActual

The area bounded by the parabola y ^2=4 ax and its latus-rectum x=a is

Options

  1. A8 3 a^2 sq. units
  2. B2 3 a^2 sq. units
  3. C4 3 a^2 sq. units
  4. D8 a ^2 aq. units

Correct answer

A. 8 3 a^2 sq. units

Step-by-step solution

Required area is shaded. Point of intersection of x=a and y^2=4 a x , is y^2=4 a^2 y= 2 a and x=a (a, 2 a) aligned & A =2 ₀^ a (2 a x ) dx & =4 a ₀^ a x ^ 1 2 dx =4 a [ x ^ 3 2 ( 3 2 ) ]₀^ a =(4 a ) ( 2 3 )( a a )= 8 3 a ^2 sq. units aligned

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