What's the non parameteric equation for the non-tilted version of this hyperbola

Question

I'm trying to derive the standard non-tilted and non parametric version of this $45^\circ$ tilted hyperbola but the lack of square terms is throwing me for a loop.

$x - xy + y + 5 = 0$

Can anyone walk me through the process?

Answer 1

Hint...if you rearrange it as $$y=\frac{x+5}{x-1}$$ you can see that the horizontal and vertical asymptotes intersect at $(1,1)$ so you need to rotate by $45^o$ about this point, not the origin.