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

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

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eccentricity (x^2)/(3^2)+(y^2)/(9^2)=1

eccentricity

\frac{x ^{2}}{3 ^{2}} + \frac{y ^{2}}{9 ^{2}} = 1

\frac{2 2}{3}

Solution steps

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

Calculate ellipse properties

\frac{x ^{2}}{3 ^{2}} + \frac{y ^{2}}{9 ^{2}} = 1 :

Ellipse with center

(h, k) = (0, 0), b = 9, a = 3

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

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

= \frac{2 2}{3}

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

\frac{x ^{2}}{81} + \frac{y ^{2}}{64} = 1

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

\frac{x ^{2}}{5 ^{2}} + \frac{y ^{2}}{1 3 ^{2}} = 1

\frac{x ^{2}}{16} + \frac{y ^{2}}{25} = 1

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