What is the eccentricity 9x^2+4y^2+54x-8y+49=0 ?

The eccentricity 9x^2+4y^2+54x-8y+49=0 is (sqrt(5))/3

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eccentricity 9x^2+4y^2+54x-8y+49=0

eccentricity

9 x^{2} + 4 y^{2} + 54 x - 8 y + 49 = 0

\frac{5}{3}

Solution steps

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

Calculate ellipse properties

9 x^{2} + 4 y^{2} + 54 x - 8 y + 49 = 0 :

Ellipse with center

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

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

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

= \frac{5}{3}

(\frac{x}{8})^{2} + (\frac{y}{6})^{2} = 1

4 x^{2} + 9 y^{2} - 8 x - 32 = 0

9 x^{2} + 6 y^{2} = 54

3 x^{2} + 10 y^{2} = 30

x^{2} + 4 y^{2} = 10

What is the eccentricity 9x^2+4y^2+54x-8y+49=0 ?
The eccentricity 9x^2+4y^2+54x-8y+49=0 is (sqrt(5))/3