What is the asymptotes of-4x^2+24x+16y^2-128y+156=0 ?

The asymptotes of-4x^2+24x+16y^2-128y+156=0 is y=(x-3)/2+4,\quad y=-(x-3)/2+4

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asymptotes of-4x^2+24x+16y^2-128y+156=0

asymptotes

- 4 x^{2} + 24 x + 16 y^{2} - 128 y + 156 = 0

y = \frac{x - 3}{2} + 4, y = - \frac{x - 3}{2} + 4

Solution steps

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

Calculate Hyperbola properties

- 4 x^{2} + 24 x + 16 y^{2} - 128 y + 156 = 0 :

Up-down Hyperbola with

(h, k) = (3, 4), a = 2, b = 4

y = \frac{2}{4} (x - 3) + 4, y = - \frac{2}{4} (x - 3) + 4

Refine

y = \frac{x - 3}{2} + 4, y = - \frac{x - 3}{2} + 4

\frac{y ^{2}}{64} - \frac{x ^{2}}{9} = 1

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

x^{2} - y^{2} + 8 x - 2 y + 14 = 0

\frac{( y - 2 ) ^{2}}{4} - \frac{( x + 3 ) ^{2}}{9} = 1

4 y^{2} - 2 x^{2} - 4 y - 8 x - 15 = 0

What is the asymptotes of-4x^2+24x+16y^2-128y+156=0 ?
The asymptotes of-4x^2+24x+16y^2-128y+156=0 is y=(x-3)/2+4,\quad y=-(x-3)/2+4