What is the asymptotes of x^2-y^2-4x+8y-21=0 ?

The asymptotes of x^2-y^2-4x+8y-21=0 is y=x+2,\quad y=-(x-2)+4

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asymptotes of x^2-y^2-4x+8y-21=0

asymptotes

x^{2} - y^{2} - 4 x + 8 y - 21 = 0

y = x + 2, y = - (x - 2) + 4

Solution steps

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

Calculate Hyperbola properties

x^{2} - y^{2} - 4 x + 8 y - 21 = 0 :

Right-left Hyperbola with

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

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

Refine

y = x + 2, y = - (x - 2) + 4

\frac{x ^{2}}{7} - \frac{7 y ^{2}}{42} = 1

\frac{x ^{2}}{81} - \frac{y ^{2}}{9} = 1

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

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

3 x^{2} - 15 y^{2} + 2 x - 3 y = 4

What is the asymptotes of x^2-y^2-4x+8y-21=0 ?
The asymptotes of x^2-y^2-4x+8y-21=0 is y=x+2,\quad y=-(x-2)+4