What is the asymptotes of (x^2}{45}-\frac{y^2)/4 =1 ?

The asymptotes of (x^2}{45}-\frac{y^2)/4 =1 is y=(2x)/(3sqrt(5)),\quad y=-(2x)/(3sqrt(5))

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asymptotes of (x^2}{45}-\frac{y^2)/4 =1

asymptotes

\frac{x ^{2}}{45} - \frac{y ^{2}}{4} = 1

y = \frac{2 x}{3 5}, y = - \frac{2 x}{3 5}

Solution steps

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

Calculate Hyperbola properties

\frac{x ^{2}}{45} - \frac{y ^{2}}{4} = 1 :

Right-left Hyperbola with

(h, k) = (0, 0), a = 35, b = 2

y = \frac{2}{3 5} (x - 0) + 0, y = - \frac{2}{3 5} (x - 0) + 0

Refine

y = \frac{2 x}{3 5}, y = - \frac{2 x}{3 5}

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

4 x^{2} - \frac{1}{2} y^{2} + 8 x + 2 y = 2

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

4 x^{2} - 9 y^{2} - 36 < 0

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

What is the asymptotes of (x^2}{45}-\frac{y^2)/4 =1 ?
The asymptotes of (x^2}{45}-\frac{y^2)/4 =1 is y=(2x)/(3sqrt(5)),\quad y=-(2x)/(3sqrt(5))