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

The eccentricity (x^2)/(8^2)+(y^2)/(3^2)=1 is (sqrt(55))/8

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eccentricity (x^2)/(8^2)+(y^2)/(3^2)=1

eccentricity

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

\frac{55}{8}

Solution steps

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

Calculate ellipse properties

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

Ellipse with center

(h, k) = (0, 0), a = 8, b = 3

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

\frac{8 ^{2} - 3 ^{2}}{8} = \frac{55}{8}

= \frac{55}{8}

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

x^{2} + 4 y^{2} - 4 x - 8 y - 92 = 0

\frac{x ^{2}}{49} + \frac{y ^{2}}{25} = 1

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

x^{2} + 4 y^{2} = 46

What is the eccentricity (x^2)/(8^2)+(y^2)/(3^2)=1 ?
The eccentricity (x^2)/(8^2)+(y^2)/(3^2)=1 is (sqrt(55))/8