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

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

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

asymptotes

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

y = \frac{2}{3} (x - 3) + 2, y = - \frac{2}{3} (x - 3) + 2

Solution steps

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

Calculate Hyperbola properties

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

Right-left Hyperbola with

(h, k) = (3, 2), a = 3, b = 2

y = \frac{2}{3} (x - 3) + 2, y = - \frac{2}{3} (x - 3) + 2

Refine

y = \frac{2}{3} (x - 3) + 2, y = - \frac{2}{3} (x - 3) + 2

- \frac{x ^{2}}{144} + \frac{y ^{2}}{25} = 1

10 y^{2} - 49 x^{2} = 490

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

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

x^{2} - 2 y^{2} + 3 x + 4 y = 2

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