What is the eccentricity (x^2)/(36)+(y^2)/(81)=1 ?

The eccentricity (x^2)/(36)+(y^2)/(81)=1 is (sqrt(5))/3

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eccentricity (x^2)/(36)+(y^2)/(81)=1

eccentricity

\frac{x ^{2}}{36} + \frac{y ^{2}}{81} = 1

\frac{5}{3}

Solution steps

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

Calculate ellipse properties

\frac{x ^{2}}{36} + \frac{y ^{2}}{81} = 1 :

Ellipse with center

(h, k) = (0, 0), b = 9, a = 6

= \frac{9 ^{2} - 6 ^{2}}{9}

\frac{9 ^{2} - 6 ^{2}}{9} = \frac{5}{3}

= \frac{5}{3}

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

What is the eccentricity (x^2)/(36)+(y^2)/(81)=1 ?
The eccentricity (x^2)/(36)+(y^2)/(81)=1 is (sqrt(5))/3