What is the eccentricity (x^2)/(25)+(y^2)/(64)=1 ?

The eccentricity (x^2)/(25)+(y^2)/(64)=1 is (sqrt(39))/8

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eccentricity (x^2)/(25)+(y^2)/(64)=1

eccentricity

\frac{x ^{2}}{25} + \frac{y ^{2}}{64} = 1

\frac{39}{8}

Solution steps

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

Calculate ellipse properties

\frac{x ^{2}}{25} + \frac{y ^{2}}{64} = 1 :

Ellipse with center

(h, k) = (0, 0), b = 8, a = 5

= \frac{8 ^{2} - 5 ^{2}}{8}

\frac{8 ^{2} - 5 ^{2}}{8} = \frac{39}{8}

= \frac{39}{8}

x^{2} + 9 y^{2} + 16 x + 18 y + 64 = 0

x^{2} + 42 y^{2} = 42

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

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

4 x^{2} + 49 y^{2} = 196

What is the eccentricity (x^2)/(25)+(y^2)/(64)=1 ?
The eccentricity (x^2)/(25)+(y^2)/(64)=1 is (sqrt(39))/8