Step 1:

Given: $ x^2 = 4ay$-------(1)

Differentiating on both sides we get,

$2x = 4ay'$

$x = 2ay'$

$a =\large\frac{ x}{2y'}$

Step 2:

Substituting in equ(1) we get

$x^2 = 4. [\large\frac{x}{2y'}] $$.y$

On simplifying and rearranging we get

$xy' -2y = 0$

This is the required equation