What is the eccentricity 3x^2+2y^2+6x-4y+5=18 ?

The eccentricity 3x^2+2y^2+6x-4y+5=18 is 1/(sqrt(3))

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eccentricity 3x^2+2y^2+6x-4y+5=18

eccentricity

3 x^{2} + 2 y^{2} + 6 x - 4 y + 5 = 18

\frac{1}{3}

Solution steps

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

Calculate ellipse properties

3 x^{2} + 2 y^{2} + 6 x - 4 y + 5 = 18 :

Ellipse with center

(h, k) = (- 1, 1), b = 3, a = 6

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

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

= \frac{1}{3}

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

3 x^{2} + 6 y^{2} = 18

9 x^{2} + 16 y^{2} - 54 x + 64 y + 1 = 0

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

4 x^{2} + 3 y^{2} - 24 x + 18 y + 51 = 0

What is the eccentricity 3x^2+2y^2+6x-4y+5=18 ?
The eccentricity 3x^2+2y^2+6x-4y+5=18 is 1/(sqrt(3))