Question
Form the differential equation representing the family of ellipses having foci on x-axis and centre at the origin.
Solution
The general equation of such ellipse is
...(1)
Differentiating w.r.t. x successively two times, we get.
...(2)
...(3)
and
...(4)
From (3), (4), we get
which is the required differential equation.
...(1)Differentiating w.r.t. x successively two times, we get.
...(2) ...(3)and
...(4)From (3), (4), we get
which is the required differential equation.
