What is the asymptotes of 9x^2-9y^2+18x+36y=63 ?

The asymptotes of 9x^2-9y^2+18x+36y=63 is y=x+3,\quad y=-(x+1)+2

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asymptotes of 9x^2-9y^2+18x+36y=63

asymptotes

9 x^{2} - 9 y^{2} + 18 x + 36 y = 63

y = x + 3, y = - (x + 1) + 2

Solution steps

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

Calculate Hyperbola properties

9 x^{2} - 9 y^{2} + 18 x + 36 y = 63 :

Right-left Hyperbola with

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

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

Refine

y = x + 3, y = - (x + 1) + 2

f (x) = x^{2} + 8 x + 12

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

x^{2} = 28 y

x = - y^{2}

9 y^{2} - 16 x^{2} = 81

What is the asymptotes of 9x^2-9y^2+18x+36y=63 ?
The asymptotes of 9x^2-9y^2+18x+36y=63 is y=x+3,\quad y=-(x+1)+2