Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
MHT CET202616 April 2026Evening ShiftMathematicsArea Under CurvesActual

The area of the region common to the parabolas 4y^2 = 9x and 3x^2 = 16y is...

Options

  1. A2 sq. units
  2. B4 sq. units
  3. C8 sq. units
  4. D16 sq. units

Correct answer

B. 4 sq. units

Step-by-step solution

The given equations of the parabolas are 4y^2 = 9x and 3x^2 = 16y . From the second equation, we have y = 3x^2 16 . Substituting this into the first equation: 4 ( 3x^2 16 )^2 = 9x 9x^4 64 = 9x x^4 - 64x = 0 x(x^3 - 64) = 0 The real roots are x = 0 and x = 4 . The required area A is the integral of the upper curve minus the lower curve from x = 0 to x = 4 : A = ₀⁴ ( 3 2 x - 3x^2 16 ) dx A = [ x^ 3/2 - x^3 16 ]₀⁴ A = ( 4^ 3/2 - 4^3 16 ) - 0 A = 8 - 4 = 4 sq. units. Answer: 4 sq. units

Practice Area Under Curves on Quantrex Academy →

More from Area Under Curves

Find the area bounded by the curve y = |2 - x| , the x –axis, and the lines x = 0 and x = 5 2026The area enclosed by the curve y = -x^2 and the line x + y + 2 = 0 is 2026The area of the region bounded by the line y = x + 2 and the curve x = -y^2 is 2026The area of the region in the first quadrant enclosed by the x -axis, the line x = 3 ,y and the circle x^2 + y^2 = 4 is 2026The area of the region bounded by the curve y^2 = x^3 , the y -axis and the lines y = 1 and y = 8 is 2026The area enclosed by the curve x = 3 , y = 3 is 2026The area in square units of the region bounded by the curve y = 16 - x^2 and lines x = 0, x = 4 above the X-axis is 2026The area bounded by the curves y = |x| - 1 and y = -|x| + 1 is 2026 Full Area Under Curves list All MHT CET PYQs