What is the eccentricity (x^2)/6+(y^2)/(12)=1 ?

The eccentricity (x^2)/6+(y^2)/(12)=1 is 1/(sqrt(2))

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eccentricity (x^2)/6+(y^2)/(12)=1

eccentricity

\frac{x ^{2}}{6} + \frac{y ^{2}}{12} = 1

\frac{1}{2}

Solution steps

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

Calculate ellipse properties

\frac{x ^{2}}{6} + \frac{y ^{2}}{12} = 1 :

Ellipse with center

(h, k) = (0, 0), b = 23, a = 6

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

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

= \frac{1}{2}

\frac{( x - 8 ) ^{2}}{9} + \frac{( y - 3 ) ^{2}}{4} = 1

9 x^{2} + 16 y^{2} - 18 x - 64 y - 71 = 0

9 x^{2} + 4 y^{2} = 36

4 x^{2} + 9 y^{2} = 36

16 x^{2} + 25 y^{2} = 400

What is the eccentricity (x^2)/6+(y^2)/(12)=1 ?
The eccentricity (x^2)/6+(y^2)/(12)=1 is 1/(sqrt(2))