What is the asymptotes of (x^2)/9-(y^2)/(49)=1 ?

The asymptotes of (x^2)/9-(y^2)/(49)=1 is y=(7x)/3 ,\quad y=-(7x)/3

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asymptotes of (x^2)/9-(y^2)/(49)=1

asymptotes

\frac{x ^{2}}{9} - \frac{y ^{2}}{49} = 1

y = \frac{7 x}{3}, y = - \frac{7 x}{3}

Solution steps

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

Calculate Hyperbola properties

\frac{x ^{2}}{9} - \frac{y ^{2}}{49} = 1 :

Right-left Hyperbola with

(h, k) = (0, 0), a = 3, b = 7

y = \frac{7}{3} (x - 0) + 0, y = - \frac{7}{3} (x - 0) + 0

Refine

y = \frac{7 x}{3}, y = - \frac{7 x}{3}

\frac{( x - 3 ) ^{2}}{49} - \frac{( y + 5 ) ^{2}}{25} = 1

25 x^{2} - 9 y^{2} = 225

\frac{( y - 3 ) ^{2}}{8 ^{2}} - \frac{( x - 2 ) ^{2}}{8 ^{2}} = 1

18 x^{2} - 32 y^{2} - 108 y - 128 x - 254 = 0

\frac{( y - 3 ) ^{2}}{49} - \frac{( x + 2 ) ^{2}}{16} = 1

What is the asymptotes of (x^2)/9-(y^2)/(49)=1 ?
The asymptotes of (x^2)/9-(y^2)/(49)=1 is y=(7x)/3 ,\quad y=-(7x)/3