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Michael_Light
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Homework Statement
P(cp , c/q) and Q(cq , c/q) are two points on the curve xy=c2. Prove that the chord PQ has an equation pqy+x=c(p+q). A variable chord of the hyperbola xy=c2 subtends a right angle at the fixed point (a,0). Show that the midpoint of the chord lies on the curve c2(x2+y2)+axy(a-2x)=0.
Homework Equations
The Attempt at a Solution
I managed to show that pqy+x=c(p+q) but failed to show that c2(x2+y2)+axy(a-2x)=0. I tried by by substituting the midpoint of points P and Q into c2(x2+y2)+axy(a-2x) but that leads to a rather complicated equation for me... another thing i can get is that ((c/p)/(cp-a))((c/q)/(cq-a))=-1 but yet, it doesn't seems to help me a lot in solving this question... can anyone give me some hints and some explanations? Thanks in advance..