COMEDK2024Evening ShiftMathematicsArea Under CurvesActual
The area of the region enclosed by the curve (x, y): 4 x^2+25 y^2=100 is
Options
- A9 sq units
- B10 sq units
- C9 5 sq units
- D16 3 sq units
Correct answer
B. 10 sq units
Step-by-step solution
The given equation is 4x^2 + 25y^2 = 100 . Dividing both sides by 100 , we get 4x^2 100 + 25y^2 100 = 1 , which simplifies to x^2 25 + y^2 4 = 1 . This is the standard equation of an ellipse x^2 a^2 + y^2 b^2 = 1 , where a^2 = 25 and b^2 = 4 . Thus, a = 5 and b = 2 . The area of an ellipse is given by the formula A = ab . Substituting the values of a and b , we get A = 5 2 = 10 sq units. Answer: 10 sq units