What is the asymptotes of x^2-y^2+8x-2y+14=0 ?

The asymptotes of x^2-y^2+8x-2y+14=0 is y=x+3,\quad y=-(x+4)-1

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asymptotes of x^2-y^2+8x-2y+14=0

asymptotes

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

y = x + 3, y = - (x + 4) - 1

Solution steps

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

Calculate Hyperbola properties

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

Right-left Hyperbola with

(h, k) = (- 4, - 1), a = 1, b = 1

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

Refine

y = x + 3, y = - (x + 4) - 1

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

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

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

9 x^{2} - 16 y^{2} - 54 x + 64 y - 127 = 0

x^{2} - 9 y^{2} = 9

What is the asymptotes of x^2-y^2+8x-2y+14=0 ?
The asymptotes of x^2-y^2+8x-2y+14=0 is y=x+3,\quad y=-(x+4)-1