What is the asymptotes of (x^2)/(16)-(y^2)/(20)=1 ?

The asymptotes of (x^2)/(16)-(y^2)/(20)=1 is y=(sqrt(5)x)/2 ,\quad y=-(sqrt(5)x)/2

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asymptotes of (x^2)/(16)-(y^2)/(20)=1

asymptotes

\frac{x ^{2}}{16} - \frac{y ^{2}}{20} = 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}}{16} - \frac{y ^{2}}{20} = 1 :

Right-left Hyperbola with

(h, k) = (0, 0), a = 4, b = 25

y = \frac{2 5}{4} (x - 0) + 0, y = - \frac{2 5}{4} (x - 0) + 0

Refine

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

y^{2} - 4 x^{2} = 16

\frac{x ^{2}}{36} - \frac{y ^{2}}{25} = 1

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

- \frac{x ^{2}}{144} + \frac{y ^{2}}{25} = 1

10 y^{2} - 49 x^{2} = 490

What is the asymptotes of (x^2)/(16)-(y^2)/(20)=1 ?
The asymptotes of (x^2)/(16)-(y^2)/(20)=1 is y=(sqrt(5)x)/2 ,\quad y=-(sqrt(5)x)/2