since the parabola has its vertex on the origin, it is in the form x² = 4ay ---- (I)
differentiating,
2x = 4ay'
x = 2ay'
y' = x/2a
now that line, x-y+3=0
y=x+3 ------------- (II)
i.e. y' at the point of contact is 1.
let the point of contact be P (x1, y1)
at P(x1,y1), y' = 1
therefore...