What is the eccentricity (x^2)/(8^2)+(y^2)/(4^2)=1 ?

The eccentricity (x^2)/(8^2)+(y^2)/(4^2)=1 is (sqrt(3))/2

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eccentricity (x^2)/(8^2)+(y^2)/(4^2)=1

eccentricity

\frac{x ^{2}}{8 ^{2}} + \frac{y ^{2}}{4 ^{2}} = 1

\frac{3}{2}

Solution steps

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

Calculate ellipse properties

\frac{x ^{2}}{8 ^{2}} + \frac{y ^{2}}{4 ^{2}} = 1 :

Ellipse with center

(h, k) = (0, 0), a = 8, b = 4

= \frac{8 ^{2} - 4 ^{2}}{8}

\frac{8 ^{2} - 4 ^{2}}{8} = \frac{3}{2}

= \frac{3}{2}

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

2 x^{2} + y^{2} - 8 y - 2 x + 1 = 0

\frac{x ^{2}}{36} + \frac{y ^{2}}{81} = 1

\frac{1}{5} x^{2} + \frac{1}{125} y^{2} = 5

3 x^{2} + 2 y^{2} = 6

What is the eccentricity (x^2)/(8^2)+(y^2)/(4^2)=1 ?
The eccentricity (x^2)/(8^2)+(y^2)/(4^2)=1 is (sqrt(3))/2