What is the asymptotes of (x-5)^2-(y-4)^2=1 ?

The asymptotes of (x-5)^2-(y-4)^2=1 is y=x-1,\quad y=-(x-5)+4

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asymptotes of (x-5)^2-(y-4)^2=1

asymptotes

(x - 5)^{2} - (y - 4)^{2} = 1

y = x - 1, y = - (x - 5) + 4

Solution steps

y = \pm \frac{b}{a} (x - h) + k

Calculate Hyperbola properties

(x - 5)^{2} - (y - 4)^{2} = 1 :

Right-left Hyperbola with

(h, k) = (5, 4), a = 1, b = 1

y = \frac{1}{1} (x - 5) + 4, y = - \frac{1}{1} (x - 5) + 4

Refine

y = x - 1, y = - (x - 5) + 4

x^{2} - 4 y^{2} - 20 x - 64 y - 172 = 0

\frac{x ^{2}}{36} - \frac{y ^{2}}{4} = 1

- 16 x^{2} + 25 y^{2} - 64 x - 150 y - 239 = 0

\frac{1}{144} x^{2} - \frac{1}{196} y^{2} = 1

9 x^{2} - 36 y^{2} = 324

What is the asymptotes of (x-5)^2-(y-4)^2=1 ?
The asymptotes of (x-5)^2-(y-4)^2=1 is y=x-1,\quad y=-(x-5)+4