What is the asymptotes of 4(x-3)^2-9(y-2)^2=36 ?

The asymptotes of 4(x-3)^2-9(y-2)^2=36 is y= 2/3 (x-3)+2,\quad y=-2/3 (x-3)+2

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asymptotes of 4(x-3)^2-9(y-2)^2=36

asymptotes

4 (x - 3)^{2} - 9 (y - 2)^{2} = 36

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

4 (x - 3)^{2} - 9 (y - 2)^{2} = 36 :

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

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

\frac{( x + 1 ) ^{2}}{3} - \frac{( y - 1 ) ^{2}}{5} = 1

9 x^{2} - 4 y^{2} + 72 x + 180 = 0

8 y^{2} - 32 x^{2} = 96

9 x^{2} - y^{2} + 36 x - 2 y = 46

What is the asymptotes of 4(x-3)^2-9(y-2)^2=36 ?
The asymptotes of 4(x-3)^2-9(y-2)^2=36 is y= 2/3 (x-3)+2,\quad y=-2/3 (x-3)+2