Could someone explain what this question really means and how to start solving it....
If m is a fixed constant such that the two families of curves and are orthogonal trajectories of each others, what must be the value of m?
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: