The functions y = g(x) and y = h(x) are orthogonal at x = a, if g'(a)h'(a) = -1.
A fraction is 1 if numerator and denominator are equal.
So you can easily solve this for m. We have:
Now, this m doesn't seem "constant", but dependent of x, c and k!
But, where do we have to look for ortogonality? At their intersection!
Let's try to find something useful, equalling both equations:
You recognise this? Filling in, in what we had for m earlier: