What is the asymptotes of 6x^2-5y^2-24x+10y-11=0 ?

The asymptotes of 6x^2-5y^2-24x+10y-11=0 is y=sqrt(6/5)(x-2)+1,\quad y=-sqrt(6/5)(x-2)+1

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asymptotes of 6x^2-5y^2-24x+10y-11=0

asymptotes

6 x^{2} - 5 y^{2} - 24 x + 10 y - 11 = 0

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

Solution steps

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

Calculate Hyperbola properties

6 x^{2} - 5 y^{2} - 24 x + 10 y - 11 = 0 :

Right-left Hyperbola with

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

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

Refine

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

x^{2} - 4 y^{2} + 2 x + 8 y - 7 = 0

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

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

y^{2} - x^{2} = 8

x^{2} - 9 y^{2} = 36

What is the asymptotes of 6x^2-5y^2-24x+10y-11=0 ?
The asymptotes of 6x^2-5y^2-24x+10y-11=0 is y=sqrt(6/5)(x-2)+1,\quad y=-sqrt(6/5)(x-2)+1