What is the eccentricity 4x^2+9y^2+32x-18y+37=0 ?

The eccentricity 4x^2+9y^2+32x-18y+37=0 is (sqrt(5))/3

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eccentricity 4x^2+9y^2+32x-18y+37=0

eccentricity

4 x^{2} + 9 y^{2} + 32 x - 18 y + 37 = 0

\frac{5}{3}

Solution steps

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

Calculate ellipse properties

4 x^{2} + 9 y^{2} + 32 x - 18 y + 37 = 0 :

Ellipse with center

(h, k) = (- 4, 1), a = 3, b = 2

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

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

= \frac{5}{3}

25 x^{2} + 9 y^{2} = 225

5 x^{2} + 7 y^{2} = 70

5 x^{2} + 10 y^{2} = 50

x^{2} + 4 y^{2} - 2 x - 16 y + 13 = 0

x^{2} = 4 y - 2 y^{2}

What is the eccentricity 4x^2+9y^2+32x-18y+37=0 ?
The eccentricity 4x^2+9y^2+32x-18y+37=0 is (sqrt(5))/3