What is the eccentricity (x^2)/4+(y^2)/(16)=1 ?

The eccentricity (x^2)/4+(y^2)/(16)=1 is (sqrt(3))/2

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eccentricity (x^2)/4+(y^2)/(16)=1

eccentricity

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

\frac{3}{2}

Solution steps

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

Calculate ellipse properties

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

Ellipse with center

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

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

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

= \frac{3}{2}

\frac{x ^{2}}{5 ^{2}} + \frac{y ^{2}}{1 3 ^{2}} = 1

\frac{x ^{2}}{16} + \frac{y ^{2}}{25} = 1

18 y^{2} + 24 y + 12 x^{2} - 12 x = 1

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

9 x^{2} + 4 y^{2} + 54 x - 8 y + 49 = 0

What is the eccentricity (x^2)/4+(y^2)/(16)=1 ?
The eccentricity (x^2)/4+(y^2)/(16)=1 is (sqrt(3))/2