Hello,

As the parabola is parallel to x axis with focus at a,0. Hence the equation of such parabola is given as:

y^2 = 4ax

Now to make the differential equation, we have to remove the a from this. So differentiate this equation one time wrt. x, because there is only one arbitrary constant.

2y .dy/dx = 4a

Now put this value of 4a in the upper equation we get the differential equation i.e.

y^2 - 2xy. dy/dx = 0

Hope it helps.