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

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

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

asymptotes

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

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

Solution steps

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

Calculate Hyperbola properties

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

16 x^{2} - 9 y^{2} - 32 x + 36 y + 124 = 0

- 3 x^{2} + 2 y^{2} + 6 x - 7 y = 7

x^{2} - 4 y^{2} = 16

x^{2} - 9 y^{2} - 4 x + 36 y - 41 = 0

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