What is the asymptotes of x^2-2y^2+3x+4y=2 ?

The asymptotes of x^2-2y^2+3x+4y=2 is y=(2x+3)/(2sqrt(2))+1,\quad y=-(2x+3)/(2sqrt(2))+1

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asymptotes of x^2-2y^2+3x+4y=2

asymptotes

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

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

Solution steps

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

Calculate Hyperbola properties

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

Right-left Hyperbola with

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

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

Refine

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

\frac{1}{4} (y + 5)^{2} - \frac{1}{16} (x + 1)^{2} = 1

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

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

x^{2} - 4 y^{2} - 8 = 0

4 y^{2} - x^{2} + 40 y - 4 x + 60 = 0

What is the asymptotes of x^2-2y^2+3x+4y=2 ?
The asymptotes of x^2-2y^2+3x+4y=2 is y=(2x+3)/(2sqrt(2))+1,\quad y=-(2x+3)/(2sqrt(2))+1