What is the asymptotes of 4x^2-9y^2-16x+18y-7=0 ?

The asymptotes of 4x^2-9y^2-16x+18y-7=0 is y=(2(x-2))/3+1,\quad y=-(2(x-2))/3+1

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asymptotes of 4x^2-9y^2-16x+18y-7=0

asymptotes

4 x^{2} - 9 y^{2} - 16 x + 18 y - 7 = 0

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

Solution steps

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

Calculate Hyperbola properties

4 x^{2} - 9 y^{2} - 16 x + 18 y - 7 = 0 :

Right-left Hyperbola with

(h, k) = (2, 1), a = \frac{7}{2}, b = \frac{14}{3}

y = \frac{\frac{14}{3}}{\frac{7}{2}} (x - 2) + 1, y = - \frac{\frac{14}{3}}{\frac{7}{2}} (x - 2) + 1

Refine

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

64 x^{2} - 100 y^{2} = 6400

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

\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

What is the asymptotes of 4x^2-9y^2-16x+18y-7=0 ?
The asymptotes of 4x^2-9y^2-16x+18y-7=0 is y=(2(x-2))/3+1,\quad y=-(2(x-2))/3+1