What is the asymptotes of (y^2)/(64)-(x^2)/(324)=1 ?

The asymptotes of (y^2)/(64)-(x^2)/(324)=1 is y=(4x)/9 ,\quad y=-(4x)/9

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asymptotes of (y^2)/(64)-(x^2)/(324)=1

asymptotes

\frac{y ^{2}}{64} - \frac{x ^{2}}{324} = 1

y = \frac{4 x}{9}, y = - \frac{4 x}{9}

Solution steps

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

Calculate Hyperbola properties

\frac{y ^{2}}{64} - \frac{x ^{2}}{324} = 1 :

Up-down Hyperbola with

(h, k) = (0, 0), a = 8, b = 18

y = \frac{8}{18} (x - 0) + 0, y = - \frac{8}{18} (x - 0) + 0

Refine

y = \frac{4 x}{9}, y = - \frac{4 x}{9}

x^{2} - 16 y^{2} = 144

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

\frac{( x + 4 ) ^{2}}{4} - \frac{( y - 1 ) ^{2}}{9} = 1

(\frac{x - 3}{4})^{2} - (\frac{y - 1}{3})^{2} = 1

x^{2} - y^{2} - 4 x - 6 y - 14 = 0

What is the asymptotes of (y^2)/(64)-(x^2)/(324)=1 ?
The asymptotes of (y^2)/(64)-(x^2)/(324)=1 is y=(4x)/9 ,\quad y=-(4x)/9