What is the differential equation fory2=4a(x−a)?

[c] Given curve is y2=4a(x−a)             ? (i) On differentiating w.r.t. x we get 2yy′=4a ⇒a=yy′2 O putting the value of a in Eq. (i) we get y2=4(yy′2)(x−yy′2)=yy′(2x−yy′) ⇒yy′(yy′−2x)+y2=0