What is the asymptotes of ((x+1)^2)/3-((y-1)^2)/5 =1 ?

The asymptotes of ((x+1)^2)/3-((y-1)^2)/5 =1 is y=sqrt(5/3)(x+1)+1,\quad y=-sqrt(5/3)(x+1)+1

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asymptotes of ((x+1)^2)/3-((y-1)^2)/5 =1

asymptotes

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

y = \frac{5}{3} (x + 1) + 1, y = - \frac{5}{3} (x + 1) + 1

Solution steps

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

Calculate Hyperbola properties

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

Right-left Hyperbola with

(h, k) = (- 1, 1), a = 3, b = 5

y = \frac{5}{3} (x - (- 1)) + 1, y = - \frac{5}{3} (x - (- 1)) + 1

Refine

y = \frac{5}{3} (x + 1) + 1, y = - \frac{5}{3} (x + 1) + 1

9 x^{2} - 4 y^{2} + 72 x + 180 = 0

8 y^{2} - 32 x^{2} = 96

9 x^{2} - y^{2} + 36 x - 2 y = 46

x^{2} - y^{2} + 6 x = 41

\frac{( y ) ^{2}}{4} - \frac{( x ) ^{2}}{16} = 1

What is the asymptotes of ((x+1)^2)/3-((y-1)^2)/5 =1 ?
The asymptotes of ((x+1)^2)/3-((y-1)^2)/5 =1 is y=sqrt(5/3)(x+1)+1,\quad y=-sqrt(5/3)(x+1)+1