The ellipse 4x^2 + 9y^2 = 1 intersects positive Y-axis at point A. If S and S' are its foci, then the area (in sq. units) of SAS' is _____

Step-by-step solution

The equation of the ellipse is x^2 1/4 + y^2 1/9 = 1 Here, a^2 = 1 4 and b^2 = 1 9 Since a > b , the major axis is along the X-axis. The eccentricity e is given by e = 1 - b^2 a^2 = 1 - 4 9 = 5 3 The foci S and S' are at ( ae, 0) = ( 5 6 , 0 ) The distance between the foci is SS' = 2ae = 5 3 The ellipse intersects the positive Y-axis at point A, so substituting x = 0 , we get y = 1 3 . Thus, A is (0, 1 3 ) The area of SAS' is 1 2 SS' OA Area = 1 2 5 3 1 3 = 5 18 sq. units. Answer: 5 18