What is x^2-3y^2+6y+6=0 ?

The solution to x^2-3y^2+6y+6=0 is Hyperbola with (h,k)=(0,1),a=sqrt(3),b=3

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x^2-3y^2+6y+6=0

x^{2} - 3 y^{2} + 6 y + 6 = 0

(h, k) = (0, 1), a = 3, b = 3

Solution steps

x^{2} - 3 y^{2} + 6 y + 6 = 0

Rewrite

x^{2} - 3 y^{2} + 6 y + 6 = 0

in the form of a standard hyperbola equation

\frac{( y - 1 ) ^{2}}{( 3 ) ^{2}} - \frac{( x - 0 ) ^{2}}{3 ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (0, 1), a = 3, b = 3

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

- 8 x^{2} + y^{2} - 32 x - 16 y = - 16

\frac{1}{2} y^{2} = 2 x^{2} - 0.02

y^{2} - 6 x^{2} + 60 x + 2 y = 173

4 (x - 2)^{2} - (y - 1)^{2} = 63

What is x^2-3y^2+6y+6=0 ?
The solution to x^2-3y^2+6y+6=0 is Hyperbola with (h,k)=(0,1),a=sqrt(3),b=3