What is the eccentricity (x^2)/4+(y^2)/9 =1 ?

The eccentricity (x^2)/4+(y^2)/9 =1 is (sqrt(5))/3

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eccentricity (x^2)/4+(y^2)/9 =1

eccentricity

\frac{x ^{2}}{4} + \frac{y ^{2}}{9} = 1

\frac{5}{3}

Solution steps

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

Calculate ellipse properties

\frac{x ^{2}}{4} + \frac{y ^{2}}{9} = 1 :

Ellipse with center

(h, k) = (0, 0), b = 3, a = 2

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

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

= \frac{5}{3}

y^{2} - 4 y + 4 x = - 16

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

x^{2} + y^{2} - 2 x + 6 y + 9 = 0

\frac{( x + 3 ) ^{2}}{16} + \frac{( y - 5 ) ^{2}}{25} = 1

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

What is the eccentricity (x^2)/4+(y^2)/9 =1 ?
The eccentricity (x^2)/4+(y^2)/9 =1 is (sqrt(5))/3