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

The solution to x^2-2y^2+3x+4y=2 is Hyperbola with (h,k)=(-3/2 ,1),a= 3/2 ,b= 3/(2sqrt(2))

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

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

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

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

z^{2} - y^{2} = 1

9 x^{2} - y^{2} + 36 = 0

- 2 x^{2} + 5 y^{2} + 3 x + 8 y + 4 = 0

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

\frac{x ^{2}}{140} - \frac{( y - 6 ) ^{2}}{4} = 1

What is x^2-2y^2+3x+4y=2 ?
The solution to x^2-2y^2+3x+4y=2 is Hyperbola with (h,k)=(-3/2 ,1),a= 3/2 ,b= 3/(2sqrt(2))