What is the asymptotes of (x^2}{16}-\frac{y^2)/4 =1 ?

The asymptotes of (x^2}{16}-\frac{y^2)/4 =1 is y= x/2 ,\quad y=-x/2

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asymptotes of (x^2}{16}-\frac{y^2)/4 =1

asymptotes

\frac{x ^{2}}{16} - \frac{y ^{2}}{4} = 1

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

Solution steps

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

Calculate Hyperbola properties

\frac{x ^{2}}{16} - \frac{y ^{2}}{4} = 1 :

Right-left Hyperbola with

(h, k) = (0, 0), a = 4, b = 2

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

Refine

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

- \frac{1}{3} (x - 3) = (y + 5)^{2}

y, x^{2} - y^{2} = 0

25 x^{2} + 9 y^{2} - 100 x + 18 y - 116 = 0

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

y^{2} = - 36 x

What is the asymptotes of (x^2}{16}-\frac{y^2)/4 =1 ?
The asymptotes of (x^2}{16}-\frac{y^2)/4 =1 is y= x/2 ,\quad y=-x/2