Calculate ellipse parameters from cone second degree equation.

Question

I'm trying to draw an ellipse basing on cone second degree equation but I have trouble in finding even basic parameters. For example I have the equation

$$1.00 x ^ 2 + -0.60 x y + 0.86 y ^ 2 + -0.29 x + -0.37 y + -0.02 = 0$$

I read here that ellipse a and b parameters can be calculated from:

$$a = \frac{1}{\sqrt{A}}$$ $$b = \frac{1}{\sqrt{B}}$$

but A and B have to be greater than 0. But Wolfram is dealing with it. Look HERE. Even if B is less than 0, Wolfram was able to draw ellipse and even name it as ellipse.

So my question is: How I can calculate things from cone second degree equation, especially ellipse $a$, $b$, $\theta$, circuit and surface area?

Answer 1

I have found this table of equations: Table of equations

Using those and Matlab I was able to determine each parameter i needed. Thx for helping me with this one :).