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

The asymptotes of 2x^2-2y^2-20x+16y-16=0 is y=x-1,\quad y=-(x-5)+4

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

asymptotes

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

y = x - 1, y = - (x - 5) + 4

Solution steps

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

Calculate Hyperbola properties

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

Right-left Hyperbola with

(h, k) = (5, 4), a = 17, b = 17

y = \frac{17}{17} (x - 5) + 4, y = - \frac{17}{17} (x - 5) + 4

Refine

y = x - 1, y = - (x - 5) + 4

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

y^{2} - x^{2} = \frac{9}{25}

25 y^{2} - 64 x^{2} = 1600

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

9 x^{2} - y^{2} + 36 x - 12 y = 36

What is the asymptotes of 2x^2-2y^2-20x+16y-16=0 ?
The asymptotes of 2x^2-2y^2-20x+16y-16=0 is y=x-1,\quad y=-(x-5)+4