What is the eccentricity 4x^2+9y^2=13 ?

The eccentricity 4x^2+9y^2=13 is (sqrt(5))/3

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eccentricity 4x^2+9y^2=13

eccentricity

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

\frac{5}{3}

Solution steps

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

Calculate ellipse properties

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

Ellipse with center

(h, k) = (0, 0), a = \frac{13}{2}, b = \frac{13}{3}

= \frac{( \frac{13}{2} ) ^{2} - ( \frac{13}{3} ) ^{2}}{\frac{13}{2}}

\frac{( \frac{13}{2} ) ^{2} - ( \frac{13}{3} ) ^{2}}{\frac{13}{2}} = \frac{5}{3}

= \frac{5}{3}

4 - x^{2} - 4 y^{2} > 0

36 x^{2} + 16 y^{2} - 180 x + 96 y - 207 = 0

2 x^{2} + y^{2} = 1

\frac{8 x ^{2}}{1} + \frac{14 y ^{2}}{1} = 122

\frac{( x - 4 ) ^{2}}{3} + \frac{y ^{2}}{9} = 1

What is the eccentricity 4x^2+9y^2=13 ?
The eccentricity 4x^2+9y^2=13 is (sqrt(5))/3