What is the eccentricity 25x^2+9y^2-100x+18y-116=0 ?

The eccentricity 25x^2+9y^2-100x+18y-116=0 is 4/5

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eccentricity 25x^2+9y^2-100x+18y-116=0

eccentricity

25 x^{2} + 9 y^{2} - 100 x + 18 y - 116 = 0

\frac{4}{5}

Solution steps

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

Calculate ellipse properties

25 x^{2} + 9 y^{2} - 100 x + 18 y - 116 = 0 :

Ellipse with center

(h, k) = (2, - 1), b = 5, a = 3

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

\frac{5 ^{2} - 3 ^{2}}{5} = \frac{4}{5}

= \frac{4}{5}

\frac{x ^{2}}{16} + \frac{y ^{2}}{36} = 1

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

10 x^{2} + 5 y^{2} = 50

9 x^{2} + 16 y^{2} - 144 = 0

\frac{x ^{2}}{36} + \frac{y ^{2}}{16} = 1

What is the eccentricity 25x^2+9y^2-100x+18y-116=0 ?
The eccentricity 25x^2+9y^2-100x+18y-116=0 is 4/5