What is the eccentricity x^2+3y^2=1 ?

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

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eccentricity x^2+3y^2=1

eccentricity

x^{2} + 3 y^{2} = 1

\frac{2}{3}

Solution steps

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

Calculate ellipse properties

x^{2} + 3 y^{2} = 1 :

Ellipse with center

(h, k) = (0, 0), a = 1, b = \frac{1}{3}

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

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

= \frac{2}{3}

\frac{x ^{2}}{9} + \frac{y ^{2}}{16} > 1

\frac{x ^{2}}{64} + \frac{y ^{2}}{100} = 1

\frac{x ^{2}}{100} + \frac{y ^{2}}{64} = 1

9 x^{2} + 25 y^{2} - 36 x - 50 y + 60 = 0

81 x^{2} - 1296 x + 16 y^{2} + 64 y = - 3952