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

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

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

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

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

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

16 x^{2} - 9 y^{2} - 96 x - 18 y - 9 = 0

x^{2} - y^{2} - 6 x + 4 y = - 4

x^{(2)} - y^{(2)} - 2 x + 4 y - 6 = 0

\frac{x ^{2}}{16} - \frac{y ^{2}}{49} = 1

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

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