What is the eccentricity (x^2)/(64)+(y^2)/(16)=1 ?

The eccentricity (x^2)/(64)+(y^2)/(16)=1 is (sqrt(3))/2

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eccentricity (x^2)/(64)+(y^2)/(16)=1

eccentricity

\frac{x ^{2}}{64} + \frac{y ^{2}}{16} = 1

\frac{3}{2}

Solution steps

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

Calculate ellipse properties

\frac{x ^{2}}{64} + \frac{y ^{2}}{16} = 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}

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

8 x^{2} + 4 y^{2} + 16 x - 12 y - 15 = 0

\frac{( x ) ^{2}}{49} + \frac{( y ) ^{2}}{36} = 1

\frac{x ^{2}}{8 ^{2}} + \frac{y ^{2}}{3 ^{2}} = 1

16 x^{2} + 4 y^{2} + 96 x - 24 y + 116 = 0

What is the eccentricity (x^2)/(64)+(y^2)/(16)=1 ?
The eccentricity (x^2)/(64)+(y^2)/(16)=1 is (sqrt(3))/2