What is the asymptotes of 4x^2-y^2-24x-4y+28=0 ?

The asymptotes of 4x^2-y^2-24x-4y+28=0 is y=2(x-3)-2,\quad y=-2(x-3)-2

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asymptotes of 4x^2-y^2-24x-4y+28=0

asymptotes

4 x^{2} - y^{2} - 24 x - 4 y + 28 = 0

y = 2 (x - 3) - 2, y = - 2 (x - 3) - 2

Solution steps

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

Calculate Hyperbola properties

4 x^{2} - y^{2} - 24 x - 4 y + 28 = 0 :

Right-left Hyperbola with

(h, k) = (3, - 2), a = 1, b = 2

y = \frac{2}{1} (x - 3) + (- 2), y = - \frac{2}{1} (x - 3) + (- 2)

Refine

y = 2 (x - 3) - 2, y = - 2 (x - 3) - 2

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

\frac{x ^{2}}{36} - \frac{y ^{2}}{16} = 1

\frac{x ^{2}}{45} - \frac{y ^{2}}{4} = 1

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

4 x^{2} - \frac{1}{2} y^{2} + 8 x + 2 y = 2

What is the asymptotes of 4x^2-y^2-24x-4y+28=0 ?
The asymptotes of 4x^2-y^2-24x-4y+28=0 is y=2(x-3)-2,\quad y=-2(x-3)-2