# How to find intersections of hyperbolas by MATLAB

Let's have two hyperbolas given by equations:
$$\mathbf{r}^T\cdot \mathbf A_1\cdot\mathbf r+\mathbf b_1^T\cdot\mathbf r+c_1=0$$ $$\mathbf{r}^T\cdot \mathbf A_2\cdot\mathbf r+\mathbf b_2^T\cdot\mathbf r+c_2=0$$ where A is 2 x 2 matrix, r and b are 2 x 1 vectors, and c is scalar.

How can I find intersections of those two hyperbolas using Matlab?
I know, that there is non-linear equation to solve, but I have no idea which function to use and how. I will be very grateful for any kind of advice.

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Since you're saying "hyperbolas", we can assume that $\mathbf r$ is a 2-vector? –  Ｊ. Ｍ. Feb 1 '12 at 0:12
Yes, you can. I hope its correct now. –  Crowley Feb 1 '12 at 0:21