What is the eccentricity 25x^2+16y^2+100x-96y-156=0 ?

The eccentricity 25x^2+16y^2+100x-96y-156=0 is 3/5

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eccentricity 25x^2+16y^2+100x-96y-156=0

eccentricity

25 x^{2} + 16 y^{2} + 100 x - 96 y - 156 = 0

\frac{3}{5}

Solution steps

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

Calculate ellipse properties

25 x^{2} + 16 y^{2} + 100 x - 96 y - 156 = 0 :

Ellipse with center

(h, k) = (- 2, 3), b = 5, a = 4

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

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

= \frac{3}{5}

18 x^{2} + 8 y^{2} + 36 x - 32 y - 22 = 0

8 x^{2} + 12 y^{2} = 96

\frac{( x ) ^{2}}{11} + \frac{( y ) ^{2}}{16} = 1

\frac{x ^{2}}{5} + \frac{y ^{2}}{4.58} = 1

3 x^{2} + 2 y^{2} - 12 x + 8 y + 19 = 0

What is the eccentricity 25x^2+16y^2+100x-96y-156=0 ?
The eccentricity 25x^2+16y^2+100x-96y-156=0 is 3/5