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

The center x^2+y^2+2x-2x+6y=0 is (0,-3)

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

center

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

(0, - 3)

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, - 3), b = 3, a = 3

And the center is:

(0, - 3)

\frac{( x + 3 ) ^{2}}{9} + \frac{( y - 1 ) ^{2}}{25} = 1

\frac{( x + 3 ) ^{2}}{25} + \frac{( y - 8 ) ^{2}}{16} = 1

x^{2} + 4 y^{2} - 6 x + 20 y - 2 = 0

19 x^{2} + y^{2} = 38

x^{2} + y^{2} + 10 y = 0