What is the asymptotes of (x^2)/4-(y^2)/(49)=1 ?

The asymptotes of (x^2)/4-(y^2)/(49)=1 is y=(7x)/2 ,\quad y=-(7x)/2

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asymptotes of (x^2)/4-(y^2)/(49)=1

asymptotes

\frac{x ^{2}}{4} - \frac{y ^{2}}{49} = 1

y = \frac{7 x}{2}, y = - \frac{7 x}{2}

Solution steps

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

Calculate Hyperbola properties

\frac{x ^{2}}{4} - \frac{y ^{2}}{49} = 1 :

Right-left Hyperbola with

(h, k) = (0, 0), a = 2, b = 7

y = \frac{7}{2} (x - 0) + 0, y = - \frac{7}{2} (x - 0) + 0

Refine

y = \frac{7 x}{2}, y = - \frac{7 x}{2}

4 y^{2} - x^{2} = 900

9 (x - 1)^{2} - 16 (y + 2)^{2} = 144

9 x^{2} - y^{2} + 6 y - 18 = 0

4 x^{2} - y^{2} - 24 x - 6 y + 23 = 0

y^{2} - x^{2} = \frac{4}{25}

What is the asymptotes of (x^2)/4-(y^2)/(49)=1 ?
The asymptotes of (x^2)/4-(y^2)/(49)=1 is y=(7x)/2 ,\quad y=-(7x)/2