What is the asymptotes of 9x^2-18x-16y^2-64y=199 ?

The asymptotes of 9x^2-18x-16y^2-64y=199 is y= 3/4 (x-1)-2,\quad y=-3/4 (x-1)-2

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asymptotes of 9x^2-18x-16y^2-64y=199

asymptotes

9 x^{2} - 18 x - 16 y^{2} - 64 y = 199

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

Solution steps

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

Calculate Hyperbola properties

9 x^{2} - 18 x - 16 y^{2} - 64 y = 199 :

Right-left Hyperbola with

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

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

\frac{x ^{2}}{4} - \frac{y ^{2}}{5} = 1

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

9 x^{2} - 4 y^{2} + 36 x - 8 y - 40 = 0

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

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

What is the asymptotes of 9x^2-18x-16y^2-64y=199 ?
The asymptotes of 9x^2-18x-16y^2-64y=199 is y= 3/4 (x-1)-2,\quad y=-3/4 (x-1)-2