Okay, I came across this question in an old mock paper. The problem is that I couldn't do it and neither could my teacher. Any help would be appreciated.

The line y=2kx cuts the curve at the points a and b. Without finding the co-ordinates of a and b, find, in terms of k, the midpoint of [ab].

Now I tried putting

and this worked down to

But I feel that would be finding the co-ordinates of a and b.

Again, any help would be appreciated.