What is the eccentricity 3x^2-6x+y^2+4y-11=0 ?

The eccentricity 3x^2-6x+y^2+4y-11=0 is sqrt(2/3)

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eccentricity 3x^2-6x+y^2+4y-11=0

eccentricity

3 x^{2} - 6 x + y^{2} + 4 y - 11 = 0

\frac{2}{3}

Solution steps

= \frac{b ^{2} - a ^{2}}{b}

Calculate ellipse properties

3 x^{2} - 6 x + y^{2} + 4 y - 11 = 0 :

Ellipse with center

(h, k) = (1, - 2), b = 32, a = 6

= \frac{( 3 2 ) ^{2} - ( 6 ) ^{2}}{3 2}

\frac{( 3 2 ) ^{2} - ( 6 ) ^{2}}{3 2} = \frac{2}{3}

= \frac{2}{3}

\frac{x ^{2}}{9} + \frac{y ^{2}}{5} = 1

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

9 x^{2} + 4 y^{2} - 18 x + 8 y - 23 = 0

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

\frac{x ^{2}}{64} + \frac{y ^{2}}{16} = 1

What is the eccentricity 3x^2-6x+y^2+4y-11=0 ?
The eccentricity 3x^2-6x+y^2+4y-11=0 is sqrt(2/3)