What is 2x^2-y^2+4x+2y-3=0 ?

The solution to 2x^2-y^2+4x+2y-3=0 is Hyperbola with (h,k)=(-1,1),a=sqrt(2),b=2

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2x^2-y^2+4x+2y-3=0

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

(h, k) = (- 1, 1), a = 2, b = 2

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (- 1, 1), a = 2, b = 2

5 x^{2} - 2 y^{2} = 9

- x^{2} + 2 y^{2} + 28 y + 14 = 0

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

9 y^{(2)} - x^{(2)} = 36

x - 3 = \frac{y ^{2} + 9}{x + 3}

What is 2x^2-y^2+4x+2y-3=0 ?
The solution to 2x^2-y^2+4x+2y-3=0 is Hyperbola with (h,k)=(-1,1),a=sqrt(2),b=2