What is the eccentricity x^2+4y^2=16 ?

The eccentricity x^2+4y^2=16 is (sqrt(3))/2

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eccentricity x^2+4y^2=16

eccentricity

x^{2} + 4 y^{2} = 16

\frac{3}{2}

Solution steps

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

Calculate ellipse properties

x^{2} + 4 y^{2} = 16 :

Ellipse with center

(h, k) = (0, 0), a = 4, b = 2

= \frac{4 ^{2} - 2 ^{2}}{4}

\frac{4 ^{2} - 2 ^{2}}{4} = \frac{3}{2}

= \frac{3}{2}

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

9 y^{2} - 25 x^{2} = 225

x^{2} - y^{2} = 4

\frac{x ^{2}}{81} + \frac{y ^{2}}{9} = 1

16 x^{2} + 16 y^{2} + 32 x + 8 y = 47

What is the eccentricity x^2+4y^2=16 ?
The eccentricity x^2+4y^2=16 is (sqrt(3))/2