What is the eccentricity 36x^2+9y^2+36y-288=0 ?

The eccentricity 36x^2+9y^2+36y-288=0 is (sqrt(3))/2

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eccentricity 36x^2+9y^2+36y-288=0

eccentricity

36 x^{2} + 9 y^{2} + 36 y - 288 = 0

\frac{3}{2}

Solution steps

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

Calculate ellipse properties

36 x^{2} + 9 y^{2} + 36 y - 288 = 0 :

Ellipse with center

(h, k) = (0, - 2), b = 6, a = 3

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

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

= \frac{3}{2}

9 x^{2} + 4 y^{2} - 54 x + 32 y + 1 = 0

16 x^{2} + 25 y^{2} - 96 x + 100 y - 156 = 0

12 x^{2} + 8 y^{2} = 96

14 x^{2} + 8 y^{2} = 112

\frac{x ^{2}}{16} + \frac{y ^{2}}{80} = 1

What is the eccentricity 36x^2+9y^2+36y-288=0 ?
The eccentricity 36x^2+9y^2+36y-288=0 is (sqrt(3))/2