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

Refine

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

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

x^{2} - y^{2} - 4 x - 6 y - 14 = 0

4 x^{2} - 9 y^{2} - 8 x + 72 y - 176 = 0

\frac{y ^{2}}{49} - \frac{x ^{2}}{64} = 1

25 x^{2} - 16 y^{2} + 50 x - 32 y - 391 = 0

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