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

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

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

asymptotes

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

y = \frac{3}{2} (x - 4) - 1, y = - \frac{3}{2} (x - 4) - 1

Solution steps

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

Calculate Hyperbola properties

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

Right-left Hyperbola with

(h, k) = (4, - 1), a = 2, b = 3

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

\frac{y ^{2}}{225} - \frac{x ^{2}}{81} = 1

9 + x^{2} - 3 y^{2} = 0

y^{2} - 4 x^{2} < 1

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

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

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