The equation of the common tangent to the equal parabola y^2=4ax and x^2=4ay is?

The tangent on y^2 = 4ax will be y = mx + a/m Since this lines touches the x^2 = 4ay.
Therefore replace y here by y = mx + a/m and simplify, You will get the quadratic in x. Now since this touches the parabola, Therfore Put D = 0. fom here you will get m = -1.
Therefore the equation of common tangent will be y = -x -a or x + y+a = 0.
Thanks.