What is the asymptotes of (x-8)^2-(y+6)^2=1 ?

The asymptotes of (x-8)^2-(y+6)^2=1 is y=x-14,\quad y=-(x-8)-6

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asymptotes of (x-8)^2-(y+6)^2=1

asymptotes

(x - 8)^{2} - (y + 6)^{2} = 1

y = x - 14, y = - (x - 8) - 6

Solution steps

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

Calculate Hyperbola properties

(x - 8)^{2} - (y + 6)^{2} = 1 :

Right-left Hyperbola with

(h, k) = (8, - 6), a = 1, b = 1

y = \frac{1}{1} (x - 8) + (- 6), y = - \frac{1}{1} (x - 8) + (- 6)

Refine

y = x - 14, y = - (x - 8) - 6

4 x^{2} - 9 y^{2} - 18 y - 153 = 0

\frac{( x - 3 ) ^{2}}{4} - \frac{( y + 5 ) ^{2}}{9} = 1

4 x^{2} - y^{2} - 8 x + 6 y - 4 = 0

4 y^{2} - 25 x^{2} = 100

+ \frac{y ^{2}}{25} - \frac{x ^{2}}{4} = 1

What is the asymptotes of (x-8)^2-(y+6)^2=1 ?
The asymptotes of (x-8)^2-(y+6)^2=1 is y=x-14,\quad y=-(x-8)-6