What is the asymptotes of 4x^2-9y^2-8x+72y-176=0 ?

The asymptotes of 4x^2-9y^2-8x+72y-176=0 is y= 2/3 (x-1)+4,\quad y=-2/3 (x-1)+4

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asymptotes of 4x^2-9y^2-8x+72y-176=0

asymptotes

4 x^{2} - 9 y^{2} - 8 x + 72 y - 176 = 0

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

Solution steps

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

Calculate Hyperbola properties

4 x^{2} - 9 y^{2} - 8 x + 72 y - 176 = 0 :

Right-left Hyperbola with

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

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

\frac{y ^{2}}{49} - \frac{x ^{2}}{64} = 1

25 x^{2} - 16 y^{2} + 50 x - 32 y - 391 = 0

\frac{( y ) ^{2}}{12} - \frac{x ^{2}}{16} = 1

9 x^{2} - 18 x - 24 y - 63 = 4 y^{2}

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

What is the asymptotes of 4x^2-9y^2-8x+72y-176=0 ?
The asymptotes of 4x^2-9y^2-8x+72y-176=0 is y= 2/3 (x-1)+4,\quad y=-2/3 (x-1)+4