What is the asymptotes of y^2-4x^2-12y-16x+16=0 ?

The asymptotes of y^2-4x^2-12y-16x+16=0 is y=2(x+2)+6,\quad y=-2(x+2)+6

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asymptotes of y^2-4x^2-12y-16x+16=0

asymptotes

y^{2} - 4 x^{2} - 12 y - 16 x + 16 = 0

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

Solution steps

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

Calculate Hyperbola properties

y^{2} - 4 x^{2} - 12 y - 16 x + 16 = 0 :

Up-down Hyperbola with

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

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

Refine

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

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

+ \frac{x ^{2}}{16} - \frac{y ^{2}}{9} = 1

9 x^{2} - 36 x - 4 y^{2} - 24 y - 36 = 0

\frac{y ^{2}}{64} - \frac{x ^{2}}{81} = 1

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

What is the asymptotes of y^2-4x^2-12y-16x+16=0 ?
The asymptotes of y^2-4x^2-12y-16x+16=0 is y=2(x+2)+6,\quad y=-2(x+2)+6