What is the asymptotes of 4x^2-9y^2-16x+54y-101=0 ?

The asymptotes of 4x^2-9y^2-16x+54y-101=0 is y= 2/3 (x-2)+3,\quad y=-2/3 (x-2)+3

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asymptotes of 4x^2-9y^2-16x+54y-101=0

asymptotes

4 x^{2} - 9 y^{2} - 16 x + 54 y - 101 = 0

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

Solution steps

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

Calculate Hyperbola properties

4 x^{2} - 9 y^{2} - 16 x + 54 y - 101 = 0 :

Right-left Hyperbola with

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

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

\frac{( x - 1 ) ^{2}}{9} - \frac{( y + 3 ) ^{2}}{4} = 1

- 4 x^{2} + y^{2} = 36

\frac{y ^{2}}{36} - \frac{x ^{2}}{9} = 1

\frac{9 x ^{2}}{64} - \frac{y ^{2}}{16} = 1

x^{2} - 4 y^{2} - 10 x - 8 y - 4 = 0

What is the asymptotes of 4x^2-9y^2-16x+54y-101=0 ?
The asymptotes of 4x^2-9y^2-16x+54y-101=0 is y= 2/3 (x-2)+3,\quad y=-2/3 (x-2)+3