COMEDK 2025 Afternoon Solved Paper

Concept:The area of an ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ is $\pi a b$ square units.Explanation:The given equation represents an ellipse with semi-major axis $a$ and semi-minor axis $b$ (assuming $a > b$).The area can be found by scaling a unit circle.A unit circle $x^2+y^2=1$ has an area of $\pi$ square units.Stretching the circle horizontally by a factor $a$ and vertically by a factor $b$ transforms it into the ellipse.Area scales by the product of the scaling factors: $a \times b$.Thus, the area of the ellipse is $\pi \times a \times b = \pi a b$.This is a standard result; no integration is required for the multiple-choice question.Answer:Option A: $\pi a b$ sq units