What is the asymptotes of (x-4)^2-(y-5)^2=15 ?

The asymptotes of (x-4)^2-(y-5)^2=15 is y=x+1,\quad y=-(x-4)+5

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asymptotes of (x-4)^2-(y-5)^2=15

asymptotes

(x - 4)^{2} - (y - 5)^{2} = 15

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

Solution steps

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

Calculate Hyperbola properties

(x - 4)^{2} - (y - 5)^{2} = 15 :

Right-left Hyperbola with

(h, k) = (4, 5), a = 15, b = 15

y = \frac{15}{15} (x - 4) + 5, y = - \frac{15}{15} (x - 4) + 5

Refine

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

\frac{x ^{2}}{81} - \frac{y ^{2}}{4} = 1

- 9 x^{2} - 32 y = - 16 y^{2} + 128

y^{2} - x^{2} = 81

x^{2} - y^{2} - 8 = 0

\frac{x ^{2}}{64} - \frac{y ^{2}}{81} = 1

What is the asymptotes of (x-4)^2-(y-5)^2=15 ?
The asymptotes of (x-4)^2-(y-5)^2=15 is y=x+1,\quad y=-(x-4)+5