Form the differential equation of the family of curves represented by the equation `(x-a)^2+2y^2=a^2` , (a being the parameter)

Explanation

` (x-a)^2+2y^2=a^2 `

`implies x^2-2ax+2y^2=0ldots`(1)

Differentiating it with respect to `x`, we get

`2x-2a+4y{dy}/{dx}=0ldots`(2)

Eliminating `a` from (1) and (2),

`2x-{x^2+2y^2}/x+4y{dy}/{dx}=0`

`implies x^2-2y^2+4xy{dy}/{dx}=0`

This is the required differential equation.