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

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

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

eccentricity

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

\frac{3}{5}

Solution steps

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

Calculate ellipse properties

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

Ellipse with center

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

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

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

= \frac{3}{5}

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

14 x^{2} + 8 y^{2} = 112

\frac{x ^{2}}{16} + \frac{y ^{2}}{80} = 1

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

4 x^{2} + 3 y^{2} + 8 x - 24 y + 51 = 0

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