What is the eccentricity 12x^2+8y^2=96 ?

The eccentricity 12x^2+8y^2=96 is 1/(sqrt(3))

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eccentricity 12x^2+8y^2=96

eccentricity

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

\frac{1}{3}

Solution steps

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

Calculate ellipse properties

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

Ellipse with center

(h, k) = (0, 0), b = 23, a = 22

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

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

= \frac{1}{3}

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

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

2 x^{2} + y^{2} = 50

4 x^{2} + 3 y^{2} + 8 x - 24 y + 51 = 0

x^{2} + y^{2} + 6 x - 4 y - 3 = 0

What is the eccentricity 12x^2+8y^2=96 ?
The eccentricity 12x^2+8y^2=96 is 1/(sqrt(3))