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 and on the rectangular hyperbola is
This was OK, my problem is the next bit...
It is given that PQ subtends a right angle at the point 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 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?