What is the eccentricity x^2+4y^2=10 ?

The eccentricity x^2+4y^2=10 is (sqrt(3))/2

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eccentricity x^2+4y^2=10

eccentricity

x^{2} + 4 y^{2} = 10

\frac{3}{2}

Solution steps

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

Calculate ellipse properties

x^{2} + 4 y^{2} = 10 :

Ellipse with center

(h, k) = (0, 0), a = 10, b = \frac{5}{2}

= \frac{( 10 ) ^{2} - ( \frac{5}{2} ) ^{2}}{10}

\frac{( 10 ) ^{2} - ( \frac{5}{2} ) ^{2}}{10} = \frac{3}{2}

= \frac{3}{2}

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

2 x^{2} + 8 y^{2} = 16

\frac{x ^{2}}{4} + \frac{y ^{2}}{3.2} = 1

9 x^{2} + 7 y^{2} = 63

\frac{x ^{2}}{49} + \frac{y ^{2}}{16} = 1

What is the eccentricity x^2+4y^2=10 ?
The eccentricity x^2+4y^2=10 is (sqrt(3))/2