What is the asymptotes of (x-4)^2-(y+1)^2=25 ?

The asymptotes of (x-4)^2-(y+1)^2=25 is y=x-5,\quad y=-(x-4)-1

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asymptotes of (x-4)^2-(y+1)^2=25

asymptotes

(x - 4)^{2} - (y + 1)^{2} = 25

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

Solution steps

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

Calculate Hyperbola properties

(x - 4)^{2} - (y + 1)^{2} = 25 :

Right-left Hyperbola with

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

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

Refine

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

- 9 x^{2} + 8 y^{2} + 36 x + 48 y = 36

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

5 x^{2} - 4 y^{2} - 20 x - 8 y = 4

4 x^{2} - 9 y^{2} = 144

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

What is the asymptotes of (x-4)^2-(y+1)^2=25 ?
The asymptotes of (x-4)^2-(y+1)^2=25 is y=x-5,\quad y=-(x-4)-1