<s>[INST] Prove that the conic $x^2 - 4xy + y^2 -2x -20y -11 = 0$ is a hyperbola and find the centre $(h,k)$ 
I have to prove that the conic $$x^2 - 4xy + y^2 -2x -20y -11 = 0$$ is a hyperbola and find the centre $(h,k)$. 

I proved it is a hyperbola using discriminant $b^2-4ac $ and the answer was greater than zero hence a hyperbola. 
But I cannot seem to change the equation into the form 
$(x-h)^2/a^2 - (y-k)^2/b^2=1$ so as to find the centre...
I could finally solve it with everyone's Help 
 [/INST] Write first the terms containing $x$ as the beginning of the square of an affine function in $x$ and $y$:
$$x^2-4xy-2x= (x-2y-1)^2-(4y+4y^2+1),$$
so that the equation becomes
\begin{align}
x^2 - 4xy + y^2 -2x -20y -11 &=  (x-2y-1)^2-(4y+4y^2+1)+y^2-20y-11 \\
&= (x-2y-1)^2-3(y^2+8y+4)\\
&=  (x-2y-1)^2-3\bigl((y+4)^2-16\bigr).
\end{align}
Can you end the calculations?
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