# Thread: I can't pretend to subtend

1. ## I can't pretend to subtend

Hi guys,

I'm having a bit of trouble understanding the word "subtends". Here's the question:

Prove that the equation of the chord joining the points $\displaystyle P(cp, c/p)$ and $\displaystyle Q(cq, c/q)$ on the rectangular hyperbola $\displaystyle xy = c^2$ is $\displaystyle pqy + x = c(p + q)$

This was OK, my problem is the next bit...

It is given that PQ subtends a right angle at the point $\displaystyle R(cr, c/r)$ on the curve. Prove that PQ is parallel to the normal at R to the curve.

I can't quite understand what this first sentance means. How does it look?
In my attachment the curve $\displaystyle xy = c^2$ is accurately drawn, but my choice of P, Q and R don't fit the requirement. I have tried moving the chord PQ around to get it parallel to a Normal at some other point R on the curve and I can't do it! It should be easy! Have I understood the meaning of the word subtend? I looked it up: "to be opposite to and delimit" but this doesn't help.

Can anyone see how this should look on the diagram?

2. Originally Posted by s_ingram

It is given that PQ subtends a right angle at the point $\displaystyle R(cr, c/r)$ on the curve. Prove that PQ is parallel to the normal at R to the curve.
It means that anglePRQ is a right angle.

3. Does it! OK. Now I'll try and figure out the proof. Thanks.