What is the eccentricity x^2+9y^2+16x+18y+64=0 ?

The eccentricity x^2+9y^2+16x+18y+64=0 is (2sqrt(2))/3

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eccentricity x^2+9y^2+16x+18y+64=0

eccentricity

x^{2} + 9 y^{2} + 16 x + 18 y + 64 = 0

\frac{2 2}{3}

Solution steps

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

Calculate ellipse properties

x^{2} + 9 y^{2} + 16 x + 18 y + 64 = 0 :

Ellipse with center

(h, k) = (- 8, - 1), a = 3, b = 1

= \frac{3 ^{2} - 1 ^{2}}{3}

\frac{3 ^{2} - 1 ^{2}}{3} = \frac{2 2}{3}

= \frac{2 2}{3}

x^{2} + 42 y^{2} = 42

\frac{( x - 4 ) ^{2}}{2} + \frac{( y - 4 ) ^{2}}{3} = 1

\frac{( x + 3 ) ^{2}}{4} + \frac{( y + 1 ) ^{2}}{1} = 1

4 x^{2} + 49 y^{2} = 196

\frac{( x + 4 ) ^{2}}{\frac{25}{4}} + (y - 6)^{2} = 1

What is the eccentricity x^2+9y^2+16x+18y+64=0 ?
The eccentricity x^2+9y^2+16x+18y+64=0 is (2sqrt(2))/3