What is the asymptotes of-4x^2+y^2=36 ?

The asymptotes of-4x^2+y^2=36 is y=2x,\quad y=-2x

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asymptotes of-4x^2+y^2=36

asymptotes

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

y = 2 x, y = - 2 x

Solution steps

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

Calculate Hyperbola properties

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

Up-down Hyperbola with

(h, k) = (0, 0), a = 6, b = 3

y = \frac{6}{3} (x - 0) + 0, y = - \frac{6}{3} (x - 0) + 0

Refine

y = 2 x, y = - 2 x

\frac{y ^{2}}{36} - \frac{x ^{2}}{9} = 1

\frac{9 x ^{2}}{64} - \frac{y ^{2}}{16} = 1

x^{2} - 4 y^{2} - 10 x - 8 y - 4 = 0

\frac{( x - 6 ) ^{2}}{48} - (y - 2)^{2} = 1

2 y^{2} - 9 x^{2} - 18 x + 20 + 5 = 0

What is the asymptotes of-4x^2+y^2=36 ?
The asymptotes of-4x^2+y^2=36 is y=2x,\quad y=-2x