What is the asymptotes of 4y^2-x^2+40y-4x+60=0 ?

The asymptotes of 4y^2-x^2+40y-4x+60=0 is y=(x+2)/2-5,\quad y=-(x+2)/2-5

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asymptotes of 4y^2-x^2+40y-4x+60=0

asymptotes

4 y^{2} - x^{2} + 40 y - 4 x + 60 = 0

y = \frac{x + 2}{2} - 5, y = - \frac{x + 2}{2} - 5

Solution steps

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

Calculate Hyperbola properties

4 y^{2} - x^{2} + 40 y - 4 x + 60 = 0 :

Up-down Hyperbola with

(h, k) = (- 2, - 5), a = 3, b = 6

y = \frac{3}{6} (x - (- 2)) + (- 5), y = - \frac{3}{6} (x - (- 2)) + (- 5)

Refine

y = \frac{x + 2}{2} - 5, y = - \frac{x + 2}{2} - 5

16 x^{2} - y^{2} = 256

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

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

- 9 x^{2} + 16 y^{2} - 90 x + 32 y - 353 = 0

x^{2} - 36 y^{2} = 36

What is the asymptotes of 4y^2-x^2+40y-4x+60=0 ?
The asymptotes of 4y^2-x^2+40y-4x+60=0 is y=(x+2)/2-5,\quad y=-(x+2)/2-5