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Let points A and B be two points on the hyperbola, xy=1, and let C be the reflection of B through the origin.

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 $xy=1.$

 Oct 11, 2019
edited by Guest  Oct 11, 2019
 #1
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Well what are your known variables?

 Oct 11, 2019
 #2
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This is the bit that seriously makes no sense.

 

"let C be the reflection of B through the origin."

 

Reflections happen across lines. I assume the line passes through the origin but whcih line are you talking about?

 

ALSO do not be so lazy when you post questions. Get rid of the meaningless $ and slashes. Make them are easily read as you are able.

 Oct 11, 2019
 #3
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Try using fact that there's a right triangle between ABA'. You're hunting for A' coordinates based off A or B coordinates. 

 

Reflecting across origin is normal, disregard other dudes rants. 

 Oct 15, 2019
 #4
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Please do not post solutions to this problem!

 

This is a homework problem, and the original poster is trying to cheat.  I know, because I am in the same class, and have the same homework.

 Oct 16, 2019
edited by Guest  Oct 16, 2019
edited by Guest  Oct 16, 2019
edited by Guest  Oct 16, 2019
edited by Guest  Oct 16, 2019

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