What is the eccentricity 9x^2+25y^2+18x+150y+9=0 ?

The eccentricity 9x^2+25y^2+18x+150y+9=0 is 4/5

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eccentricity 9x^2+25y^2+18x+150y+9=0

eccentricity

9 x^{2} + 25 y^{2} + 18 x + 150 y + 9 = 0

\frac{4}{5}

Solution steps

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

Calculate ellipse properties

9 x^{2} + 25 y^{2} + 18 x + 150 y + 9 = 0 :

Ellipse with center

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

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

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

= \frac{4}{5}

16 x^{2} + 80 y^{2} = 1280

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

4 x^{2} + 9 y^{2} = 13

4 - x^{2} - 4 y^{2} > 0

36 x^{2} + 16 y^{2} - 180 x + 96 y - 207 = 0

What is the eccentricity 9x^2+25y^2+18x+150y+9=0 ?
The eccentricity 9x^2+25y^2+18x+150y+9=0 is 4/5