Your game plan is a good one.
I gave it a quick try and got into a mess at step 4, too.
I'll work on it and try to get back to you.
I was just wondering for this question:
A variable normal to xy = c^2 meets the x-axis and y-axis at P, Q. Show that the locus of midpoint of PQ is
1. Find equ. of normal.
2. Find P + Q.
3. Find midpoint.
4. Somehow manipulate midpoint coordinates to get locus.
I just wanted to make sure that it is the right method because it seems to me to be pretty messy since my P + Q are kinda yucky already so by the time I got to step 4...*shudders*
To check whether the given problem is correct or not, select a numerical problem.
Let the given equation be xy = 4. Draw a normal at (1, 4).
Then find the mid point of PQ and substitute in the given expression. See whether it satisfies or not.