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?
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You mean you want it on the form $y=f(x)$? Or do you want to turn it $45^\circ$, then express it on the form $\frac{(x-a)^2}{b}-\frac{(y-c)^2}{d}=1$? Or is there some other form you want to have it in? – Arthur Apr 01 '18 at 22:28
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I was looking for $\frac{(x - h)^2}{a^2} - \frac{(y -k)^2}{b^2} = 1$ after it was rotated back 45 degrees. – benleis Apr 01 '18 at 22:33
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If you’ve performed the rotation correctly, you should end up with squared terms. – amd Apr 01 '18 at 22:43
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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.
David Quinn
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