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

The asymptotes of (x^2)/(a^2)-(y^2)/(b^2)=1 is y=(bx)/a ,\quad y=-(bx)/a

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asymptotes of (x^2)/(a^2)-(y^2)/(b^2)=1

asymptotes

\frac{x ^{2}}{a ^{2}} - \frac{y ^{2}}{b ^{2}} = 1

y = \frac{b x}{a}, y = - \frac{b x}{a}

Solution steps

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

Calculate Hyperbola properties

\frac{x ^{2}}{a ^{2}} - \frac{y ^{2}}{b ^{2}} = 1 :

Right-left Hyperbola with

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

y = \frac{b}{a} (x - 0) + 0, y = - \frac{b}{a} (x - 0) + 0

Refine

y = \frac{b x}{a}, y = - \frac{b x}{a}

9 y^{2} - 36 x^{2} = 324

\frac{y ^{2}}{25} - \frac{x ^{2}}{81} = 1

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

x^{2} - 4 y^{2} - 2 x + 16 y = 20

9 y^{2} - x^{2} + 2 x + 54 y + 62 = 0

What is the asymptotes of (x^2)/(a^2)-(y^2)/(b^2)=1 ?
The asymptotes of (x^2)/(a^2)-(y^2)/(b^2)=1 is y=(bx)/a ,\quad y=-(bx)/a