What is the asymptotes of 4y^2-2x^2+24y-8x-9=0 ?

The asymptotes of 4y^2-2x^2+24y-8x-9=0 is y=(x+2)/(sqrt(2))-3,\quad y=-(x+2)/(sqrt(2))-3

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asymptotes of 4y^2-2x^2+24y-8x-9=0

asymptotes

4 y^{2} - 2 x^{2} + 24 y - 8 x - 9 = 0

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

Solution steps

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

Calculate Hyperbola properties

4 y^{2} - 2 x^{2} + 24 y - 8 x - 9 = 0 :

Up-down Hyperbola with

(h, k) = (- 2, - 3), a = \frac{37}{2}, b = \frac{37}{2}

y = \frac{\frac{37}{2}}{\frac{37}{2}} (x - (- 2)) + (- 3), y = - \frac{\frac{37}{2}}{\frac{37}{2}} (x - (- 2)) + (- 3)

Refine

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

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

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

16 x^{2} - 9 y^{2} - 32 x + 36 y + 124 = 0

- 3 x^{2} + 2 y^{2} + 6 x - 7 y = 7

x^{2} - 4 y^{2} = 16

What is the asymptotes of 4y^2-2x^2+24y-8x-9=0 ?
The asymptotes of 4y^2-2x^2+24y-8x-9=0 is y=(x+2)/(sqrt(2))-3,\quad y=-(x+2)/(sqrt(2))-3