What is the asymptotes of ((x+2)^2)/4-((y-1)^2)/9 =1 ?

The asymptotes of ((x+2)^2)/4-((y-1)^2)/9 =1 is y= 3/2 (x+2)+1,\quad y=-3/2 (x+2)+1

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asymptotes of ((x+2)^2)/4-((y-1)^2)/9 =1

asymptotes

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

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

Solution steps

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

Calculate Hyperbola properties

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

Right-left Hyperbola with

(h, k) = (- 2, 1), a = 2, b = 3

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

Refine

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

4 x^{2} - 25 y^{2} + 100 y = 200

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

9 y^{2} - 49 x^{2} = 441

4 x^{2} - 9 y^{2} - 16 x + 18 y - 7 = 0

64 x^{2} - 100 y^{2} = 6400

What is the asymptotes of ((x+2)^2)/4-((y-1)^2)/9 =1 ?
The asymptotes of ((x+2)^2)/4-((y-1)^2)/9 =1 is y= 3/2 (x+2)+1,\quad y=-3/2 (x+2)+1