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

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

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

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

(h, k) = (- 1, - 1), a = 3, b = 3

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (- 1, - 1), a = 3, b = 3

(x - 3)^{2} = 8 + (y + 5)^{2}

\frac{( x + 3 ) ^{2}}{9} - \frac{( y - 3 ) ^{2}}{16} = 1

4 x^{2} + 8 x - 4 y^{2} + 12 y - 3 = 0

\frac{( x + 4 ) ^{2}}{16} - \frac{( y - 2 ) ^{2}}{36} = 1

12 y^{2} + 72 y - 4 x^{2} + 16 x + 44 = 0

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