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

The center x^2+y^2-6+2y+6=0 is (0,-1)

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

center

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

(0, - 1)

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, - 1), b = 1, a = 1

And the center is:

(0, - 1)

2 x^{2} + 3 y^{2} + 4 x = 1

16 x^{2} + 4 y^{2} - 32 x + 24 y - 12 = 0

x^{2} + y^{2} - 12 y = 0

\frac{( x - 1 ) ^{2}}{6} + \frac{( y - 3 ) ^{2}}{2} = 1

x^{2} + 3 y^{2} = 1