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
- A1 2 ( -2) sq. units
- B3 2 ( -2) sq. units
- C5 4 ( -2) sq. units
- 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