What is the eccentricity 6x^2+9y^2=54 ?

The eccentricity 6x^2+9y^2=54 is 1/(sqrt(3))

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eccentricity 6x^2+9y^2=54

eccentricity

6 x^{2} + 9 y^{2} = 54

\frac{1}{3}

Solution steps

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

Calculate ellipse properties

6 x^{2} + 9 y^{2} = 54 :

Ellipse with center

(h, k) = (0, 0), a = 3, b = 6

= \frac{3 ^{2} - ( 6 ) ^{2}}{3}

\frac{3 ^{2} - ( 6 ) ^{2}}{3} = \frac{1}{3}

= \frac{1}{3}

10 x^{2} + 35 y^{2} = 5

\frac{x ^{2}}{13.44} + \frac{y ^{2}}{16} = 1

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

25 x^{2} + 9 y^{2} - 150 x - 18 y + 9 = 0

\frac{x ^{2}}{169} + \frac{y ^{2}}{144} = 1

What is the eccentricity 6x^2+9y^2=54 ?
The eccentricity 6x^2+9y^2=54 is 1/(sqrt(3))