What is the asymptotes of 4x^2-9y^2-18y-153=0 ?

The asymptotes of 4x^2-9y^2-18y-153=0 is y=(2x)/3-1,\quad y=-(2x)/3-1

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asymptotes of 4x^2-9y^2-18y-153=0

asymptotes

4 x^{2} - 9 y^{2} - 18 y - 153 = 0

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

Solution steps

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

Calculate Hyperbola properties

4 x^{2} - 9 y^{2} - 18 y - 153 = 0 :

Right-left Hyperbola with

(h, k) = (0, - 1), a = 6, b = 4

y = \frac{4}{6} (x - 0) + (- 1), y = - \frac{4}{6} (x - 0) + (- 1)

Refine

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

\frac{( x - 3 ) ^{2}}{4} - \frac{( y + 5 ) ^{2}}{9} = 1

4 x^{2} - y^{2} - 8 x + 6 y - 4 = 0

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

+ \frac{y ^{2}}{25} - \frac{x ^{2}}{4} = 1

\frac{( y - 2 ) ^{2}}{9} - \frac{( x + 3 ) ^{2}}{1} = 1

What is the asymptotes of 4x^2-9y^2-18y-153=0 ?
The asymptotes of 4x^2-9y^2-18y-153=0 is y=(2x)/3-1,\quad y=-(2x)/3-1