Any help on this question will be greatly apprectiated.
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 \(\Gamma\) be the circumcircle of \(\triangle ABC\) and let A' be the point on \(\Gamma\) diametrically opposite A. Show that A' is also on the hyperbola xy=1.
Note: A hint came with this question: Assign coordinates to A and B. Then you should be able to find the coordinates of C. You can also find the coordinates of A' if you think carefully - there's something special about that point that makes its coordinates easier to find. Btw I just got (a), I still need help on (b) though.
Again, help is greatly valued.
Here is some work I did: I drew a graph and noticed that \(\triangle A'BC \) is right since it is in the semi-circle of circle \(\Gamma\). Someone told me to progress with that idea since I'm probably close to the answer but I don't know how to.
Please do not discuss this problem! This is an active homework problem.
To the original poster: I realize that homework may be challenging. If you wish to receive some help from the staff or other students, I encourage you to use the resources that the online classes provide, such as the Message Board. Thanks.
I am not against helping you to learn (with hints) and maybe I will later if i look properly and want to.
One thing that I think detracts from personal improvement of problem solving is the ease with which students can get help and answers.
This is not all bad but it takes time to learn problem solving. Each problem must be thought about really hard and if you get your own brain waves that has to be better in every way than to just get answers and hints handed to you on a silver platter.
This is why your school is so scathing of you getting outside help.