What is the asymptotes of 4y^2-5x^2-48y-10x+59=0 ?

The asymptotes of 4y^2-5x^2-48y-10x+59=0 is y=(sqrt(5)(x+1))/2+6,\quad y=-(sqrt(5)(x+1))/2+6

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asymptotes of 4y^2-5x^2-48y-10x+59=0

asymptotes

4 y^{2} - 5 x^{2} - 48 y - 10 x + 59 = 0

y = \frac{5 ( x + 1 )}{2} + 6, y = - \frac{5 ( x + 1 )}{2} + 6

Solution steps

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

Calculate Hyperbola properties

4 y^{2} - 5 x^{2} - 48 y - 10 x + 59 = 0 :

Up-down Hyperbola with

(h, k) = (- 1, 6), a = 25, b = 4

y = \frac{2 5}{4} (x - (- 1)) + 6, y = - \frac{2 5}{4} (x - (- 1)) + 6

Refine

y = \frac{5 ( x + 1 )}{2} + 6, y = - \frac{5 ( x + 1 )}{2} + 6

9 x^{2} - 4 y^{2} - 36 x + 72 = 0

16 x^{2} - 25 y^{2} = 400

9 y^{2} - 5 x^{2} + 72 y + 30 x + 54 = 0

\frac{( y - 3 ) ^{2}}{9} - \frac{x ^{2}}{25} = 1

\frac{x ^{2}}{12} - \frac{y ^{2}}{16} = 1

What is the asymptotes of 4y^2-5x^2-48y-10x+59=0 ?
The asymptotes of 4y^2-5x^2-48y-10x+59=0 is y=(sqrt(5)(x+1))/2+6,\quad y=-(sqrt(5)(x+1))/2+6