What is the eccentricity 9x^2+25y^2+108x-200y+499=0 ?

The eccentricity 9x^2+25y^2+108x-200y+499=0 is 4/5

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eccentricity 9x^2+25y^2+108x-200y+499=0

eccentricity

9 x^{2} + 25 y^{2} + 108 x - 200 y + 499 = 0

\frac{4}{5}

Solution steps

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

Calculate ellipse properties

9 x^{2} + 25 y^{2} + 108 x - 200 y + 499 = 0 :

Ellipse with center

(h, k) = (- 6, 4), a = 5, b = 3

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

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

= \frac{4}{5}

x^{2} + 2 y^{2} - 2 x + 8 y + 5 = 0

\frac{x ^{2}}{8} + \frac{y ^{2}}{4} = 1

\frac{x ^{2}}{144} + \frac{y ^{2}}{169} = 1

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

\frac{( x ) ^{2}}{12} + \frac{( y ) ^{2}}{16} = 1

What is the eccentricity 9x^2+25y^2+108x-200y+499=0 ?
The eccentricity 9x^2+25y^2+108x-200y+499=0 is 4/5