What is the asymptotes of x^2-y^2+6x=41 ?

The asymptotes of x^2-y^2+6x=41 is y=x+3,\quad y=-(x+3)

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asymptotes of x^2-y^2+6x=41

asymptotes

x^{2} - y^{2} + 6 x = 41

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

Solution steps

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

Calculate Hyperbola properties

x^{2} - y^{2} + 6 x = 41 :

Right-left Hyperbola with

(h, k) = (- 3, 0), a = 52, b = 52

y = \frac{5 2}{5 2} (x - (- 3)) + 0, y = - \frac{5 2}{5 2} (x - (- 3)) + 0

Refine

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

\frac{( y ) ^{2}}{4} - \frac{( x ) ^{2}}{16} = 1

(x - 8)^{2} - (y + 6)^{2} = 1

4 x^{2} - 9 y^{2} - 18 y - 153 = 0

\frac{( x - 3 ) ^{2}}{4} - \frac{( y + 5 ) ^{2}}{9} = 1

4 x^{2} - y^{2} - 8 x + 6 y - 4 = 0

What is the asymptotes of x^2-y^2+6x=41 ?
The asymptotes of x^2-y^2+6x=41 is y=x+3,\quad y=-(x+3)