MHT CET202520 Apr 2025Evening ShiftMathematicsArea Under CurvesActual
AOB is the positive quadrant of the ellipse x^2 25 + y^2 9 =1 in which OA =5, OB =3 . The area between the arc AB and the chord AB of the ellipse in sq.units is
Options
- A3 5 ( -2)
- B15 2 ( -2)
- C3 10 ( -2)
- D15 4 ( -2)
Correct answer
D. 15 4 ( -2)
Step-by-step solution
The ellipse equation is x^2 25 + y^2 9 = 1 , so a = 5 and b = 3 . The quadrant area is 1 4 a b = 15 4 . The right triangle OAB with vertices (0,0) , (5,0) , and (0,3) has area 1 2 5 3 = 15 2 . The area between arc and chord AB is 15 4 - 15 2 = 15( - 2) 4 , matching option D.