What is the eccentricity 9x^2+6y^2=54 ?

The eccentricity 9x^2+6y^2=54 is 1/(sqrt(3))

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eccentricity 9x^2+6y^2=54

eccentricity

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

\frac{1}{3}

Solution steps

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

Calculate ellipse properties

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

Ellipse with center

(h, k) = (0, 0), b = 3, a = 6

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

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

= \frac{1}{3}

3 x^{2} + 10 y^{2} = 30

x^{2} + 4 y^{2} = 10

\frac{y ^{2}}{16} + \frac{x ^{2}}{9} = 1

2 x^{2} + 8 y^{2} = 16

\frac{x ^{2}}{4} + \frac{y ^{2}}{3.2} = 1

What is the eccentricity 9x^2+6y^2=54 ?
The eccentricity 9x^2+6y^2=54 is 1/(sqrt(3))