What is the eccentricity 6x^2-12x+54y^2+108y-426=0 ?

The eccentricity 6x^2-12x+54y^2+108y-426=0 is (2sqrt(2))/3

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eccentricity 6x^2-12x+54y^2+108y-426=0

eccentricity

6 x^{2} - 12 x + 54 y^{2} + 108 y - 426 = 0

\frac{2 2}{3}

Solution steps

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

Calculate ellipse properties

6 x^{2} - 12 x + 54 y^{2} + 108 y - 426 = 0 :

Ellipse with center

(h, k) = (1, - 1), a = 9, b = 3

= \frac{9 ^{2} - 3 ^{2}}{9}

\frac{9 ^{2} - 3 ^{2}}{9} = \frac{2 2}{3}

= \frac{2 2}{3}

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

6 x^{2} + 9 y^{2} = 54

10 x^{2} + 35 y^{2} = 5

\frac{x ^{2}}{13.44} + \frac{y ^{2}}{16} = 1

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

What is the eccentricity 6x^2-12x+54y^2+108y-426=0 ?
The eccentricity 6x^2-12x+54y^2+108y-426=0 is (2sqrt(2))/3