Finding The Focus Point Of $y = \frac{1}{x}$

Question

Hello everyone How can I calculate the focus point of $y = \frac{1}{x}$?

I converted the equation to $xy = 1$ and from there I tried to convert the function to something like this: $Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0$ but I didn't success.