What is the asymptotes of ((x-2)^2)/4-((y+3)^2)/5 =1 ?

The asymptotes of ((x-2)^2)/4-((y+3)^2)/5 =1 is y=(sqrt(5))/2 (x-2)-3,\quad y=-(sqrt(5))/2 (x-2)-3

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asymptotes of ((x-2)^2)/4-((y+3)^2)/5 =1

asymptotes

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

y = \frac{5}{2} (x - 2) - 3, y = - \frac{5}{2} (x - 2) - 3

Solution steps

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

Calculate Hyperbola properties

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

Right-left Hyperbola with

(h, k) = (2, - 3), a = 2, b = 5

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

\frac{( x + 2 ) ^{2}}{36} - y^{2} = 1

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

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

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

x = x^{2} - \frac{y ^{2}}{9}

What is the asymptotes of ((x-2)^2)/4-((y+3)^2)/5 =1 ?
The asymptotes of ((x-2)^2)/4-((y+3)^2)/5 =1 is y=(sqrt(5))/2 (x-2)-3,\quad y=-(sqrt(5))/2 (x-2)-3