What is the asymptotes of 9x^2-16y^2-54x+64y-127=0 ?

The asymptotes of 9x^2-16y^2-54x+64y-127=0 is y= 3/4 (x-3)+2,\quad y=-3/4 (x-3)+2

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asymptotes of 9x^2-16y^2-54x+64y-127=0

asymptotes

9 x^{2} - 16 y^{2} - 54 x + 64 y - 127 = 0

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

Solution steps

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

Calculate Hyperbola properties

9 x^{2} - 16 y^{2} - 54 x + 64 y - 127 = 0 :

Right-left Hyperbola with

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

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

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

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

\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

What is the asymptotes of 9x^2-16y^2-54x+64y-127=0 ?
The asymptotes of 9x^2-16y^2-54x+64y-127=0 is y= 3/4 (x-3)+2,\quad y=-3/4 (x-3)+2