What is the asymptotes of 16y^2-32y-9x^2-18x=137 ?

The asymptotes of 16y^2-32y-9x^2-18x=137 is y= 3/4 (x+1)+1,\quad y=-3/4 (x+1)+1

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asymptotes of 16y^2-32y-9x^2-18x=137

asymptotes

16 y^{2} - 32 y - 9 x^{2} - 18 x = 137

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

Solution steps

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

Calculate Hyperbola properties

16 y^{2} - 32 y - 9 x^{2} - 18 x = 137 :

Up-down Hyperbola with

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

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

Refine

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

\frac{x ^{2}}{a ^{2}} - \frac{y ^{2}}{b ^{2}} = 1

9 y^{2} - 36 x^{2} = 324

\frac{y ^{2}}{25} - \frac{x ^{2}}{81} = 1

9 y^{2} - 25 x^{2} = 225

x^{2} - 4 y^{2} - 2 x + 16 y = 20

What is the asymptotes of 16y^2-32y-9x^2-18x=137 ?
The asymptotes of 16y^2-32y-9x^2-18x=137 is y= 3/4 (x+1)+1,\quad y=-3/4 (x+1)+1