What is the asymptotes of-9x^2+4y^2-36x-16y-164=0 ?

The asymptotes of-9x^2+4y^2-36x-16y-164=0 is y=(3(x+2))/2+2,\quad y=-(3(x+2))/2+2

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asymptotes of-9x^2+4y^2-36x-16y-164=0

asymptotes

- 9 x^{2} + 4 y^{2} - 36 x - 16 y - 164 = 0

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

Solution steps

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

Calculate Hyperbola properties

- 9 x^{2} + 4 y^{2} - 36 x - 16 y - 164 = 0 :

Up-down Hyperbola with

(h, k) = (- 2, 2), a = 6, b = 4

y = \frac{6}{4} (x - (- 2)) + 2, y = - \frac{6}{4} (x - (- 2)) + 2

Refine

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

\frac{y ^{2}}{16} - \frac{x ^{2}}{36} = 1

x^{2} - y^{2} - 4 x + 8 y - 21 = 0

\frac{x ^{2}}{7} - \frac{7 y ^{2}}{42} = 1

\frac{x ^{2}}{81} - \frac{y ^{2}}{9} = 1

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

What is the asymptotes of-9x^2+4y^2-36x-16y-164=0 ?
The asymptotes of-9x^2+4y^2-36x-16y-164=0 is y=(3(x+2))/2+2,\quad y=-(3(x+2))/2+2