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

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

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

asymptotes

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

y = 2 (x - 5) - 1, y = - 2 (x - 5) - 1

Solution steps

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

Calculate Hyperbola properties

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

Up-down Hyperbola with

(h, k) = (5, - 1), a = 4, b = 2

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

Refine

y = 2 (x - 5) - 1, y = - 2 (x - 5) - 1

25 x^{2} - 9 y^{2} = 225

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

f (x) = x^{2} + 4 x + 4

x = 4 y^{2}

9 x^{2} + 4 y^{2} = 36

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