What is the asymptotes of (x^2)/4-(y^2)/5 =1 ?

The asymptotes of (x^2)/4-(y^2)/5 =1 is y=(sqrt(5)x)/2 ,\quad y=-(sqrt(5)x)/2

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asymptotes of (x^2)/4-(y^2)/5 =1

asymptotes

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

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

Solution steps

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

Calculate Hyperbola properties

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

Right-left Hyperbola with

(h, k) = (0, 0), a = 2, b = 5

y = \frac{5}{2} (x - 0) + 0, y = - \frac{5}{2} (x - 0) + 0

Refine

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

x^{2} - y^{2} + 4 x - 6 y = 6

9 x^{2} - 4 y^{2} + 36 x - 8 y - 40 = 0

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

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

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

What is the asymptotes of (x^2)/4-(y^2)/5 =1 ?
The asymptotes of (x^2)/4-(y^2)/5 =1 is y=(sqrt(5)x)/2 ,\quad y=-(sqrt(5)x)/2