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?
Ok, so far so good! You know have m/(...) = 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: