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

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

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

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

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

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

- x^{2} + 4 y^{2} + 2 x + 24 y + 31 = 0

9 x^{2} - 16 y^{2} - 18 x + 64 y - 199 = 0

3631 + 896 x - 54 y = 9 y^{2} - 64 x^{2}

4 x^{2} - 16 y^{2} - 64 = 0

3 y^{2} - 3 x^{2} - 15 = 0

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