What is the asymptotes of (9x^2)/(64)-(y^2)/(16)=1 ?

The asymptotes of (9x^2)/(64)-(y^2)/(16)=1 is y=(3x)/2 ,\quad y=-(3x)/2

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asymptotes of (9x^2)/(64)-(y^2)/(16)=1

asymptotes

\frac{9 x ^{2}}{64} - \frac{y ^{2}}{16} = 1

y = \frac{3 x}{2}, y = - \frac{3 x}{2}

Solution steps

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

Calculate Hyperbola properties

\frac{9 x ^{2}}{64} - \frac{y ^{2}}{16} = 1 :

Right-left Hyperbola with

(h, k) = (0, 0), a = \frac{8}{3}, b = 4

y = \frac{4}{\frac{8}{3}} (x - 0) + 0, y = - \frac{4}{\frac{8}{3}} (x - 0) + 0

Refine

y = \frac{3 x}{2}, y = - \frac{3 x}{2}

x^{2} - 4 y^{2} - 10 x - 8 y - 4 = 0

\frac{( x - 6 ) ^{2}}{48} - (y - 2)^{2} = 1

2 y^{2} - 9 x^{2} - 18 x + 20 + 5 = 0

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

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

What is the asymptotes of (9x^2)/(64)-(y^2)/(16)=1 ?
The asymptotes of (9x^2)/(64)-(y^2)/(16)=1 is y=(3x)/2 ,\quad y=-(3x)/2