What is the asymptotes of (x^2)/3-(y^2)/(1.5)=1 ?

The asymptotes of (x^2)/3-(y^2)/(1.5)=1 is y=sqrt((1.5)/3)x,\quad y=-sqrt((1.5)/3)x

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asymptotes of (x^2)/3-(y^2)/(1.5)=1

asymptotes

\frac{x ^{2}}{3} - \frac{y ^{2}}{1.5} = 1

y = \frac{1.5}{3} x, y = - \frac{1.5}{3} x

Solution steps

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

Calculate Hyperbola properties

\frac{x ^{2}}{3} - \frac{y ^{2}}{1.5} = 1 :

Right-left Hyperbola with

(h, k) = (0, 0), a = 3, b = 1.5

y = \frac{1.5}{3} (x - 0) + 0, y = - \frac{1.5}{3} (x - 0) + 0

Refine

y = \frac{1.5}{3} x, y = - \frac{1.5}{3} x

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

4 x^{2} - 9 y^{2} - 16 x + 54 y - 101 = 0

\frac{( x - 1 ) ^{2}}{9} - \frac{( y + 3 ) ^{2}}{4} = 1

- 4 x^{2} + y^{2} = 36

\frac{y ^{2}}{36} - \frac{x ^{2}}{9} = 1

What is the asymptotes of (x^2)/3-(y^2)/(1.5)=1 ?
The asymptotes of (x^2)/3-(y^2)/(1.5)=1 is y=sqrt((1.5)/3)x,\quad y=-sqrt((1.5)/3)x