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AP EAMCET202021 Sep 2020Morning ShiftMathematicsParabolaActual

If the area bounded by the parabola (y^2=16 a x ) and the line (y=4 m x ) is ( a^2 12 ) sq. units, then the value of ' (m ) ' is

Options

  1. A-1
  2. B1
  3. C0
  4. D2

Correct answer

D. 2

Step-by-step solution

Equation of given parabola (y^2=16 a x ) and the line (y=4 m x ) On simplifying the equation of parabola and line, the (y )-coordinate of point (A ) is ( 4 a m ) ( ) The area bounded by given curves ( aligned & = ₀^ 4 a m ( y 4 m - y^2 16 a ) d y= a^2 12 (given) & [ y^2 8 m - y^3 48 a ]₀^ 4 a m = a^2 12 & 16 a^2 8 m^3 - 64 a^3 48 m^3 a = a^2 12 & 2 m^3 - 4 3 m^3 = 1 12 & 6-4 3 m^3 = 1 12 & m^2=8 m=2 aligned ) Hence, option (d) is correct.

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