Conic sections

  • Thread starter splac6996
  • Start date
  • #1
37
0

Main Question or Discussion Point

I have a hyperbola with the following equation and I am trying to find my angles to eventually rotate this (conic section), but I don't know what to do because when I follow the standard form of (A-C)/B, I get zero. Is there some trick that I don't know about.

x^2+4xy+y^2=12
 

Answers and Replies

  • #2
7
0
First, you can write the equation in this way
[tex]
\left[ \begin{array}{cc}
x & y
\end{array} \right]
\cdot
\left[ \begin{array}{cc}
1 & 2 \\
2 & 1
\end{array} \right]
\cdot
\left[ \begin{array}{c}
x \\ y
\end{array} \right] = 12
[/tex]

Now, you have to diagonalize the symmetric matrix
[tex]
A = \left[ \begin{array}{cc}
1 & 2 \\
2 & 1
\end{array} \right]
[/tex]

Then, see this!
 
  • #3
37
0
I have never seen this technique before is that the only way to do this?
 

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