What is the eccentricity 36x^2+5y^2-90y-495=0 ?

The eccentricity 36x^2+5y^2-90y-495=0 is (sqrt(31))/6

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eccentricity 36x^2+5y^2-90y-495=0

eccentricity

36 x^{2} + 5 y^{2} - 90 y - 495 = 0

\frac{31}{6}

Solution steps

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

Calculate ellipse properties

36 x^{2} + 5 y^{2} - 90 y - 495 = 0 :

Ellipse with center

(h, k) = (0, 9), b = 65, a = 5

= \frac{( 6 5 ) ^{2} - 5 ^{2}}{6 5}

\frac{( 6 5 ) ^{2} - 5 ^{2}}{6 5} = \frac{31}{6}

= \frac{31}{6}

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

\frac{x ^{2}}{6} + \frac{y ^{2}}{12} = 1

\frac{( x - 8 ) ^{2}}{9} + \frac{( y - 3 ) ^{2}}{4} = 1

9 x^{2} + 16 y^{2} - 18 x - 64 y - 71 = 0

9 x^{2} + 4 y^{2} = 36

What is the eccentricity 36x^2+5y^2-90y-495=0 ?
The eccentricity 36x^2+5y^2-90y-495=0 is (sqrt(31))/6