What is the eccentricity 18x^2+8y^2+36x-32y-22=0 ?

The eccentricity 18x^2+8y^2+36x-32y-22=0 is (sqrt(5))/3

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

eccentricity

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

\frac{5}{3}

Decimal

0.74535 \dots

Solution steps

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

Calculate ellipse properties

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

Ellipse with center

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

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

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

= \frac{5}{3}

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

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

\frac{x ^{2}}{196} + \frac{y ^{2}}{121} = 1

\frac{x ^{2}}{5} + \frac{y ^{2}}{20.98} = 1

16 x^{2} + 192 x + 576 + 25 y^{2} = 1600

What is the eccentricity 18x^2+8y^2+36x-32y-22=0 ?
The eccentricity 18x^2+8y^2+36x-32y-22=0 is (sqrt(5))/3