What is the asymptotes of 2y^2-9x^2-18x+20+5=0 ?

The asymptotes of 2y^2-9x^2-18x+20+5=0 is y=(3(x+1))/(sqrt(2)),\quad y=-(3(x+1))/(sqrt(2))

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asymptotes of 2y^2-9x^2-18x+20+5=0

asymptotes

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

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

Solution steps

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

Calculate Hyperbola properties

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

Right-left Hyperbola with

(h, k) = (- 1, 0), a = \frac{34}{3}, b = 17

y = \frac{17}{\frac{34}{3}} (x - (- 1)) + 0, y = - \frac{17}{\frac{34}{3}} (x - (- 1)) + 0

Refine

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

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

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

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

x^{2} - 5 y^{2} = 7

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

What is the asymptotes of 2y^2-9x^2-18x+20+5=0 ?
The asymptotes of 2y^2-9x^2-18x+20+5=0 is y=(3(x+1))/(sqrt(2)),\quad y=-(3(x+1))/(sqrt(2))