What is the asymptotes of 9x^2-18x-24y-63=4y^2 ?

The asymptotes of 9x^2-18x-24y-63=4y^2 is y= 3/2 (x-1)-3,\quad y=-3/2 (x-1)-3

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asymptotes of 9x^2-18x-24y-63=4y^2

asymptotes

9 x^{2} - 18 x - 24 y - 63 = 4 y^{2}

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

Solution steps

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

Calculate Hyperbola properties

9 x^{2} - 18 x - 24 y - 63 = 4 y^{2} :

Right-left Hyperbola with

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

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

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

3 x^{2} - 8 y^{2} + 12 x + 16 y + 20 = 0

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

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

- 9 x^{2} + 4 y^{2} = 36

What is the asymptotes of 9x^2-18x-24y-63=4y^2 ?
The asymptotes of 9x^2-18x-24y-63=4y^2 is y= 3/2 (x-1)-3,\quad y=-3/2 (x-1)-3