Question
Form the differential equation of the family of ellipses having foci on y-axis and centre at origin.
Solution
The equation of family of ellipses having foci on y-axis and centre at origin is
...(1)
Differentiating w.r.t. x, we get,
...(2)
...(3)
Again differentiating (2) w.r.t.x, we get,
...(4)
From (3) and (4), we get,
which is required differential equation.
...(1)Differentiating w.r.t. x, we get,
...(2) ...(3)Again differentiating (2) w.r.t.x, we get,
...(4)From (3) and (4), we get,
which is required differential equation.
