If the two ends of the major axis of an ellipse are (5, 0) and (-5, 0) and one focus lies on the line 3x - 5y - 9 = 0 , then its equation is

Step-by-step solution

The ends of the major axis are given as (5, 0) and (-5, 0) . This implies that the center of the ellipse is at the origin (0, 0) and the semi-major axis is a = 5 . The foci of the ellipse lie on the major axis, which is the x-axis. Thus, the coordinates of the foci are of the form ( ae, 0) . It is given that one focus lies on the line 3x - 5y - 9 = 0 . Substituting y = 0 into the equation of the line: 3x - 5(0) - 9 = 0 3x = 9 x = 3 So, one focus is at (3, 0) , which means ae = 3 . Using the relation b^2 = a^2(1 - e