The solution to the intersection point can only be found numerically so it is next to impossible to find an expression for a that way. However we can be tricky.

First we are looking for a point x such that f(x) = g(x). That is we have a point x = b on the functions f(x) and g(x) such that

Now, perpendicular slopes follow the rule that m' = -1/m. So we are looking for a at the intersection point such that

Evaluate this at x = b and see if you can use the intersection condition to write this equation as a function of a only.

-Dan