What is the eccentricity 4x^2+9y^2-16x+18y=11 ?

The eccentricity 4x^2+9y^2-16x+18y=11 is (sqrt(5))/3

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eccentricity 4x^2+9y^2-16x+18y=11

eccentricity

4 x^{2} + 9 y^{2} - 16 x + 18 y = 11

\frac{5}{3}

Solution steps

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

Calculate ellipse properties

4 x^{2} + 9 y^{2} - 16 x + 18 y = 11 :

Ellipse with center

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

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

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

= \frac{5}{3}

4 x^{2} + 3 y^{2} - 8 x + 18 y + 19 = 0

x^{2} + 4 y^{2} - 6 x + 20 y - 2 = 0

\frac{x ^{2}}{25} + \frac{( y + 3 ) ^{2}}{49} = 1

36 x^{2} + 9 y^{2} + 36 y - 288 = 0

9 x^{2} + 4 y^{2} - 54 x + 32 y + 1 = 0

What is the eccentricity 4x^2+9y^2-16x+18y=11 ?
The eccentricity 4x^2+9y^2-16x+18y=11 is (sqrt(5))/3