What is the eccentricity 36x^2+16y^2-180x+96y-207=0 ?

The eccentricity 36x^2+16y^2-180x+96y-207=0 is (sqrt(5))/3

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eccentricity 36x^2+16y^2-180x+96y-207=0

eccentricity

36 x^{2} + 16 y^{2} - 180 x + 96 y - 207 = 0

\frac{5}{3}

Decimal

0.74535 \dots

Solution steps

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

Calculate ellipse properties

36 x^{2} + 16 y^{2} - 180 x + 96 y - 207 = 0 :

Ellipse with center

(h, k) = (\frac{5}{2}, - 3), b = 6, a = 4

= \frac{6 ^{2} - 4 ^{2}}{6}

\frac{6 ^{2} - 4 ^{2}}{6} = \frac{5}{3}

= \frac{5}{3}

\frac{( x - 4 ) ^{2}}{3} + \frac{y ^{2}}{9} = 1

\frac{x ^{2}}{16} + \frac{y ^{2}}{4} = 1

\frac{( x - 4 ) ^{2}}{5} + \frac{( y - 2 ) ^{2}}{4} = 1

49 x^{2} - 98 x + 64 y^{2} + 256 y - 2831 = 0

\frac{( x ^{2} )}{16} + \frac{( y ^{2} )}{25} = 1

What is the eccentricity 36x^2+16y^2-180x+96y-207=0 ?
The eccentricity 36x^2+16y^2-180x+96y-207=0 is (sqrt(5))/3