Prove: QR Passes Through O If PQ, PR on xy=c2 Inclined Equally

[Michael_Light]

Homework Statement

Given that P,Q and R lie on the hyperbola xy=c², prove that if PQ and PR inclined equally to the coordinate axes, then QR passes through O.

Homework Equations

The Attempt at a Solution

I don't understand what does ''PQ and PR are inclined equally to the coordinate axes'' means.. can anyone explain?

 

[eumyang]

This means that their slopes are opposites, I believe. In other words, if the slope of PQ is m, then the slope of PR is -m.

 

[genericusrnme]

I'd have to say, it sounds to me like the slope along x = slope along y, it's symmetric under swapping x and y