Let A and B be two points on the hyperbola xy=1, and let C be the reflection of B through the origin.
(a) Show that C is on the hyperbola.
(b) Let Γ be the circumcircle of triangle ABC and let A' be the point on Γ diametrically opposite A. Show that A' is also on the hyperbola xy=1.
I don't know where to start. I tried graphing it but it doesn't make any sense to me. Thanks for any help!