What is the eccentricity (x^2)/(5^2)+(y^2)/(13^2)=1 ?

The eccentricity (x^2)/(5^2)+(y^2)/(13^2)=1 is 12/13

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eccentricity (x^2)/(5^2)+(y^2)/(13^2)=1

eccentricity

\frac{x ^{2}}{5 ^{2}} + \frac{y ^{2}}{1 3 ^{2}} = 1

\frac{12}{13}

Solution steps

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

Calculate ellipse properties

\frac{x ^{2}}{5 ^{2}} + \frac{y ^{2}}{1 3 ^{2}} = 1 :

Ellipse with center

(h, k) = (0, 0), b = 13, a = 5

= \frac{1 3 ^{2} - 5 ^{2}}{13}

\frac{1 3 ^{2} - 5 ^{2}}{13} = \frac{12}{13}

= \frac{12}{13}

\frac{x ^{2}}{16} + \frac{y ^{2}}{25} = 1

18 y^{2} + 24 y + 12 x^{2} - 12 x = 1

+ 9 x^{2} + 4 y^{2} = 36

9 x^{2} + 4 y^{2} + 54 x - 8 y + 49 = 0

(\frac{x}{8})^{2} + (\frac{y}{6})^{2} = 1

What is the eccentricity (x^2)/(5^2)+(y^2)/(13^2)=1 ?
The eccentricity (x^2)/(5^2)+(y^2)/(13^2)=1 is 12/13