Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
MHT CET202520 Apr 2025Morning ShiftMathematicsArea Under CurvesActual

The area of the region bounded by x^2 9 + y^2 4 =1 and the line x 3 + y 2 =1 is

Options

  1. A1 2 ( -2) sq. units
  2. B3 2 ( -2) sq. units
  3. C5 4 ( -2) sq. units
  4. D2 3 ( -2) sq. units

Correct answer

B. 3 2 ( -2) sq. units

Step-by-step solution

Area bounded by ellipse and line in first quadrant The ellipse x^2 9 + y^2 4 =1 has semi-axes a=3 and b=2 , with x-intercept (3,0) and y-intercept (0,2) . The line x 3 + y 2 =1 passes through these same intercepts, forming a triangle with coordinate axes. The region bounded by the ellipse and line corresponds to the quarter-elliptical area in the first quadrant minus this triangular area. The total elliptical area is A_ ellipse = ab = (3)(2) = 6 , so the first quadrant portion is 6 4 = 3 2 . The triangle formed by

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