1. A variable chord of the hyperbola xy=c(sq.) subtends a right angle at the fixed point (h, 0). Show that that the mid-point of the chord lies on the curve c2(x2+y2)=hxy(2x-h).

2. The points P (cp, c/p) and R (cr, c/r) are located on the rectangular hyperbola xy=c(sq.). Prove that the chord PR has the equation pry+x=c(p+r).

Mid-year's are tomorrow, and I'm stuck at these--help!