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

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

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

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

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

Solution steps

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

Rewrite

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

4 x^{2} + 16 x - 25 y^{2} + 50 y - 109 = 0

\frac{y ^{2}}{36} - \frac{x ^{2}}{14} = 1

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

\frac{x ^{2}}{16} - \frac{y ^{2}}{20} = 1

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

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