What is the eccentricity 4-x^2-4y^2>0 ?

The eccentricity 4-x^2-4y^2>0 is (sqrt(3))/2

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eccentricity 4-x^2-4y^2>0

eccentricity

4 - x^{2} - 4 y^{2} > 0

\frac{3}{2}

Solution steps

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

Rewrite as

4 - x^{2} - 4 y^{2} = 0

Calculate ellipse properties

4 - x^{2} - 4 y^{2} = 0 :

Ellipse with center

(h, k) = (0, 0), a = 2, b = 1

= \frac{2 ^{2} - 1 ^{2}}{2}

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

= \frac{3}{2}

36 x^{2} + 16 y^{2} - 180 x + 96 y - 207 = 0

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

\frac{8 x ^{2}}{1} + \frac{14 y ^{2}}{1} = 122

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

\frac{x ^{2}}{16} + \frac{y ^{2}}{4} = 1

What is the eccentricity 4-x^2-4y^2>0 ?
The eccentricity 4-x^2-4y^2>0 is (sqrt(3))/2