Prove that the locus of midpoints of parallel chords of xy = c^2 is a diameter.
Is anyone able to give me some hints on how to do this question?
You can easily show that its gradient is .
A set of parallel chords will all have the same gradient, , say. So:
, where is a constant. Call this equation (1).The mid-point of satisfies:
Now, using equation (1), find an equation connecting and , and show that this, the locus of the mid-point of , is a straight line through the origin.
Can you complete it now?