Find the equation of the common tangent to the parabola y^2 = 4ax ,x^2 = 4by.

My thinking on this is to solve each equation for y, and find the point where the two functions are equal, then proceed to take partials and use them as vectors for the equation of a tangent line. However the algebra gets very messy and I am not sure if I am doing it right. Can I see how one of you would handle this problem?

Much regards,