Hello UltraGirlConsider the chord joining to .

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:

and

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?

Grandad