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

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

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

eccentricity

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

\frac{1}{3}

Solution steps

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

Calculate ellipse properties

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

Ellipse with center

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

\frac{( x ) ^{2}}{11} + \frac{( y ) ^{2}}{16} = 1

\frac{x ^{2}}{5} + \frac{y ^{2}}{4.58} = 1

3 x^{2} + 2 y^{2} - 12 x + 8 y + 19 = 0

\frac{x ^{2}}{196} + \frac{y ^{2}}{121} = 1

\frac{x ^{2}}{5} + \frac{y ^{2}}{20.98} = 1

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