I've done this
Let the tangent is y = mx + c
Substitute this into parabola's equation with y^2 = 4ax.
So: (mx + c)^2 = 4ax
There is only one root because tangent meets parabola at only one point.
From this equation we found mc = a
Same thing for x^2 = 4ay.
By solving two equations simultaneously, we get the tangent equation,
y + x +a = 0.