What is the eccentricity 4x^2+9y^2=36 ?

The eccentricity 4x^2+9y^2=36 is (sqrt(5))/3

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eccentricity 4x^2+9y^2=36

eccentricity

4 x^{2} + 9 y^{2} = 36

\frac{5}{3}

Solution steps

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

Calculate ellipse properties

4 x^{2} + 9 y^{2} = 36 :

Ellipse with center

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

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

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

= \frac{5}{3}

4 x^{2} + 3 y^{2} - 24 x + 18 y + 51 = 0

\frac{x ^{2}}{36} + \frac{y ^{2}}{49} = 1

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

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

+ 36 x^{2} + y^{2} = 36

What is the eccentricity 4x^2+9y^2=36 ?
The eccentricity 4x^2+9y^2=36 is (sqrt(5))/3