What is the asymptotes of 5x^2-6y^2-20x+12y-16=0 ?

The asymptotes of 5x^2-6y^2-20x+12y-16=0 is y=sqrt(5/6)(x-2)+1,\quad y=-sqrt(5/6)(x-2)+1

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asymptotes of 5x^2-6y^2-20x+12y-16=0

asymptotes

5 x^{2} - 6 y^{2} - 20 x + 12 y - 16 = 0

y = \frac{5}{6} (x - 2) + 1, y = - \frac{5}{6} (x - 2) + 1

Solution steps

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

Calculate Hyperbola properties

5 x^{2} - 6 y^{2} - 20 x + 12 y - 16 = 0 :

Right-left Hyperbola with

(h, k) = (2, 1), a = 6, b = 5

y = \frac{5}{6} (x - 2) + 1, y = - \frac{5}{6} (x - 2) + 1

Refine

y = \frac{5}{6} (x - 2) + 1, y = - \frac{5}{6} (x - 2) + 1

\frac{y ^{2}}{1 2 ^{2}} - \frac{x ^{2}}{6 ^{2}} = 1

x^{2} - 4 (y - 3)^{2} = 4

16 y^{2} - 81 x^{2} - 256 y + 486 x = 1001

4 x^{2} - y^{2} + 40 x - 4 y + 80 = 0

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

What is the asymptotes of 5x^2-6y^2-20x+12y-16=0 ?
The asymptotes of 5x^2-6y^2-20x+12y-16=0 is y=sqrt(5/6)(x-2)+1,\quad y=-sqrt(5/6)(x-2)+1