What is the asymptotes of x^2-5y^2=7 ?

The asymptotes of x^2-5y^2=7 is y= x/(sqrt(5)),\quad y=-x/(sqrt(5))

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asymptotes of x^2-5y^2=7

asymptotes

x^{2} - 5 y^{2} = 7

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

Solution steps

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

Calculate Hyperbola properties

x^{2} - 5 y^{2} = 7 :

Right-left Hyperbola with

(h, k) = (0, 0), a = 7, b = \frac{7}{5}

y = \frac{\frac{7}{5}}{7} (x - 0) + 0, y = - \frac{\frac{7}{5}}{7} (x - 0) + 0

Refine

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

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

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

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

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

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

What is the asymptotes of x^2-5y^2=7 ?
The asymptotes of x^2-5y^2=7 is y= x/(sqrt(5)),\quad y=-x/(sqrt(5))