What is the eccentricity 1/5 x^2+1/125 y^2=5 ?

The eccentricity 1/5 x^2+1/125 y^2=5 is (2sqrt(6))/5

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eccentricity 1/5 x^2+1/125 y^2=5

eccentricity

\frac{1}{5} x^{2} + \frac{1}{125} y^{2} = 5

\frac{2 6}{5}

Solution steps

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

Calculate ellipse properties

\frac{1}{5} x^{2} + \frac{1}{125} y^{2} = 5 :

Ellipse with center

(h, k) = (0, 0), b = 25, a = 5

= \frac{2 5 ^{2} - 5 ^{2}}{25}

\frac{2 5 ^{2} - 5 ^{2}}{25} = \frac{2 6}{5}

= \frac{2 6}{5}

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

3 x^{2} + 7 y^{2} = 63

\frac{x ^{2}}{160} + \frac{y ^{2}}{16} = 1

9 x^{2} + 25 y^{2} + 108 x - 200 y + 499 = 0

x^{2} + 2 y^{2} - 2 x + 8 y + 5 = 0

What is the eccentricity 1/5 x^2+1/125 y^2=5 ?
The eccentricity 1/5 x^2+1/125 y^2=5 is (2sqrt(6))/5