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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?

Marcin Iwanieec
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  • $A = 1.00 > 0$ and $B = 0.86 > 0$, so what's the problem? $B$ is the term that multiplies $y^2$, not the one that multiplies $xy$... – the_candyman Oct 08 '15 at 10:24
  • Ohh.. indeed! In other equation i was looking, B was standing next to xy. That solved problem partially. Now i can calculate angle and even center point. But what if ellipse's A and B are both negative? That mean we have an imaginary ellipse. How that could be drawn, like Wolfram is doing it? – Marcin Iwanieec Oct 08 '15 at 11:31
  • If you have $$-0.4 x^2- 0.9 y^2 = 0$$ is the same as $$0.4 x^2+ 0.9 y^2 = 0$$, right? – the_candyman Oct 08 '15 at 11:38
  • Yes. I have induced that info to my code. But i have still problem determine the equations for theta. – Marcin Iwanieec Oct 08 '15 at 16:40

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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 :).

Marcin Iwanieec
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