What is the asymptotes of 16x^2-9y^2-32x+36y+124=0 ?

The asymptotes of 16x^2-9y^2-32x+36y+124=0 is y= 4/3 (x-1)+2,\quad y=-4/3 (x-1)+2

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asymptotes of 16x^2-9y^2-32x+36y+124=0

asymptotes

16 x^{2} - 9 y^{2} - 32 x + 36 y + 124 = 0

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

Solution steps

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

Calculate Hyperbola properties

16 x^{2} - 9 y^{2} - 32 x + 36 y + 124 = 0 :

Up-down Hyperbola with

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

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

- 3 x^{2} + 2 y^{2} + 6 x - 7 y = 7

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

x^{2} - 9 y^{2} - 4 x + 36 y - 41 = 0

\frac{y ^{2}}{64} - \frac{x ^{2}}{324} = 1

x^{2} - 16 y^{2} = 144

What is the asymptotes of 16x^2-9y^2-32x+36y+124=0 ?
The asymptotes of 16x^2-9y^2-32x+36y+124=0 is y= 4/3 (x-1)+2,\quad y=-4/3 (x-1)+2