What is the center 11x^2+3x+3y^2+11y=0 ?

The center 11x^2+3x+3y^2+11y=0 is (-3/22 ,-11/6)

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center 11x^2+3x+3y^2+11y=0

center

11 x^{2} + 3 x + 3 y^{2} + 11 y = 0

(- \frac{3}{22}, - \frac{11}{6})

Solution steps

11 x^{2} + 3 x + 3 y^{2} + 11 y = 0

Rewrite

11 x^{2} + 3 x + 3 y^{2} + 11 y = 0

in the form of the standard ellipse equation

\frac{( x - ( - \frac{3}{22} ) ) ^{2}}{( \frac{679}{11 6} ) ^{2}} + \frac{( y - ( - \frac{11}{6} ) ) ^{2}}{( \frac{679}{3 22} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- \frac{3}{22}, - \frac{11}{6}), a = \frac{679}{11 6}, b = \frac{679}{3 22}

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (- \frac{3}{22}, - \frac{11}{6}), b = \frac{679}{3 22}, a = \frac{679}{11 6}

And the center is:

(- \frac{3}{22}, - \frac{11}{6})

16 x^{2} + 81 y^{2} = 81

9 x^{2} + 16 y^{2} - 18 x + 96 y - 279 = 0

4 x^{2} + 9 y^{2} - 24 x - 36 y = - 36

20 x^{2} - 16 y^{2} - 40 x 128 x - 556 = 0

\frac{( x + 1 ) ^{2}}{4} + \frac{( y - 2 ) ^{2}}{9} = 1

What is the center 11x^2+3x+3y^2+11y=0 ?
The center 11x^2+3x+3y^2+11y=0 is (-3/22 ,-11/6)