# How to satisfy this identity (conformal model in geometric algebra)

1. Sep 9, 2011

### mnb96

Hello,

I have the following equation in x and y: $$xy - \sqrt{(x^2+a^2)(y^2+c^2)} = -\frac{1}{a^2}-\frac{1}{c^2}$$ where the quantities a2 and c2 are given real constants, and I have to find real values for x, and y such that the equation above is always satisfied.

Actually, I know that the solution should be: $x = \frac{1-a^2}{2}$, $y = \frac{1-c^2}{2}$, but I would like to know if there is a "mechanical" procedure to arrive at that solution, or if one has just to do "trial and error".

PS: for anyone interested, solving this equation is useful for constructing the conformal model in Geometric Algebra.

Last edited: Sep 9, 2011
2. Sep 9, 2011

### mathman

Have you tried putting xy on the other side and then squaring both sides? The (xy)2 term will cancel.