What is the eccentricity 5/81 x^2+(y^2)/9 =1 ?

The eccentricity 5/81 x^2+(y^2)/9 =1 is 2/3

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eccentricity 5/81 x^2+(y^2)/9 =1

eccentricity

\frac{5}{81} x^{2} + \frac{y ^{2}}{9} = 1

\frac{2}{3}

Solution steps

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

Calculate ellipse properties

\frac{5}{81} x^{2} + \frac{y ^{2}}{9} = 1 :

Ellipse with center

(h, k) = (0, 0), a = \frac{9}{5}, b = 3

= \frac{( \frac{9}{5} ) ^{2} - 3 ^{2}}{\frac{9}{5}}

\frac{( \frac{9}{5} ) ^{2} - 3 ^{2}}{\frac{9}{5}} = \frac{2}{3}

= \frac{2}{3}

3 x^{2} + y^{2} - 24 x = - 39

9 x^{2} + 25 y^{2} + 18 x + 150 y + 9 = 0

16 x^{2} + 80 y^{2} = 1280

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

4 x^{2} + 9 y^{2} = 13

What is the eccentricity 5/81 x^2+(y^2)/9 =1 ?
The eccentricity 5/81 x^2+(y^2)/9 =1 is 2/3