The differential equation representing the family of ellipses having foci either on the x -axis or on the y -axis, center at the origin and passing through the point 0 , 3 is

Step-by-step solution

Let the equation of ellipse be x 2 a 2 + y 2 b 2 = 1 It passes through 0 , 3 ⇒ x 2 a 2 + y 2 9 = 1     . . . i Differentiating w.r.t. x , ⇒ 2 x a 2 + 2 y 9 d y d x = 0 1 a 2 = - y 9 x y '     . . . ii From i and ii we get, - x y 9 y ' + y 2 9 = 1 ⇒ x y y ' - y 2 + 9 = 0