What is the eccentricity (x^2)/(16)+(y^2)/(36)=1 ?

The eccentricity (x^2)/(16)+(y^2)/(36)=1 is (sqrt(5))/3

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eccentricity (x^2)/(16)+(y^2)/(36)=1

eccentricity

\frac{x ^{2}}{16} + \frac{y ^{2}}{36} = 1

\frac{5}{3}

Solution steps

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

Calculate ellipse properties

\frac{x ^{2}}{16} + \frac{y ^{2}}{36} = 1 :

Ellipse with center

(h, k) = (0, 0), b = 6, a = 4

= \frac{6 ^{2} - 4 ^{2}}{6}

\frac{6 ^{2} - 4 ^{2}}{6} = \frac{5}{3}

= \frac{5}{3}

\frac{x ^{2}}{8} + \frac{y ^{2}}{3} = 1

10 x^{2} + 5 y^{2} = 50

9 x^{2} + 16 y^{2} - 144 = 0

\frac{x ^{2}}{36} + \frac{y ^{2}}{16} = 1

4 x^{2} + 9 y^{2} - 16 x + 18 y = 11

What is the eccentricity (x^2)/(16)+(y^2)/(36)=1 ?
The eccentricity (x^2)/(16)+(y^2)/(36)=1 is (sqrt(5))/3