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

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

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

asymptotes

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

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

Solution steps

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

Calculate Hyperbola properties

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

Right-left Hyperbola with

(h, k) = (- 5, 0), a = 2, b = 2

y = \frac{2}{2} (x - (- 5)) + 0, y = - \frac{2}{2} (x - (- 5)) + 0

Refine

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

\frac{x ^{2}}{25} - \frac{y ^{2}}{16} = 1

2 x^{2} - 2 y^{2} - 20 x + 16 y + 16 = 0

25 y^{2} - 16 x^{2} - 400 = 0

9 (y - 2)^{2} - 4 x^{2} = 36

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

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