What is the eccentricity 4x^2+9y^2=144 ?

The eccentricity 4x^2+9y^2=144 is (sqrt(5))/3

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eccentricity 4x^2+9y^2=144

eccentricity

4 x^{2} + 9 y^{2} = 144

\frac{5}{3}

Solution steps

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

Calculate ellipse properties

4 x^{2} + 9 y^{2} = 144 :

Ellipse with center

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

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

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

= \frac{5}{3}

\frac{x ^{2}}{16} + \frac{y ^{2}}{81} = 1

(y + 2)^{2} = 1 - 2 (x + 1)^{2}

\frac{x ^{2}}{5} + \frac{y ^{2}}{8} = 1

18 x^{2} + 4 y^{2} - 72 x + 4 y + 37 = 0

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

What is the eccentricity 4x^2+9y^2=144 ?
The eccentricity 4x^2+9y^2=144 is (sqrt(5))/3