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 = 1, b = 1

y = \frac{1}{1} (x - 5) + 4, y = - \frac{1}{1} (x - 5) + 4

Refine

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

25 y^{2} - 16 x^{2} - 400 = 0

9 (y - 2)^{2} - 4 x^{2} = 36

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

4 x^{2} - 9 y^{2} - 36 = 0

\frac{y ^{2}}{16} - \frac{x ^{2}}{25} = 1

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