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

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

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eccentricity 4x^2+y^2=16

eccentricity

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

\frac{3}{2}

Solution steps

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

Calculate ellipse properties

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

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}

x^{2} + y^{2} - 6 x - 8 y = 50

\frac{x ^{2}}{3 ^{2}} + \frac{y ^{2}}{9 ^{2}} = 1

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

\frac{x ^{2}}{81} + \frac{y ^{2}}{64} = 1

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

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