Hello.

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?

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- April 16th 2010, 06:06 PMUltraGirl[SOLVED] Hyperbola 3
Hello.

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? - April 17th 2010, 11:23 AMGrandad
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:

Can you complete it now?

Grandad