What is the asymptotes of 5x^2-5y^2+20x-60y=185 ?

The asymptotes of 5x^2-5y^2+20x-60y=185 is y=x-4,\quad y=-(x+2)-6

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asymptotes of 5x^2-5y^2+20x-60y=185

asymptotes

5 x^{2} - 5 y^{2} + 20 x - 60 y = 185

y = x - 4, y = - (x + 2) - 6

Solution steps

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

Calculate Hyperbola properties

5 x^{2} - 5 y^{2} + 20 x - 60 y = 185 :

Right-left Hyperbola with

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

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

Refine

y = x - 4, y = - (x + 2) - 6

9 y^{2} - 4 x^{2} - 36 y - 8 x = 4

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

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

\frac{y ^{2}}{49} - \frac{x ^{2}}{36} = 1

\frac{x ^{2}}{49} - \frac{y ^{2}}{36} = 1

What is the asymptotes of 5x^2-5y^2+20x-60y=185 ?
The asymptotes of 5x^2-5y^2+20x-60y=185 is y=x-4,\quad y=-(x+2)-6