What is the eccentricity (x^2)/(2^2)+(y^2)/(9^2)=1 ?

The eccentricity (x^2)/(2^2)+(y^2)/(9^2)=1 is (sqrt(77))/9

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eccentricity (x^2)/(2^2)+(y^2)/(9^2)=1

eccentricity

\frac{x ^{2}}{2 ^{2}} + \frac{y ^{2}}{9 ^{2}} = 1

\frac{77}{9}

Solution steps

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

Calculate ellipse properties

\frac{x ^{2}}{2 ^{2}} + \frac{y ^{2}}{9 ^{2}} = 1 :

Ellipse with center

(h, k) = (0, 0), b = 9, a = 2

= \frac{9 ^{2} - 2 ^{2}}{9}

\frac{9 ^{2} - 2 ^{2}}{9} = \frac{77}{9}

= \frac{77}{9}

25 x^{2} + 9 y^{2} - 150 x - 18 y + 9 = 0

\frac{x ^{2}}{169} + \frac{y ^{2}}{144} = 1

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

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

4 x^{2} + 25 y^{2} - 40 x + 150 y + 225 = 0

What is the eccentricity (x^2)/(2^2)+(y^2)/(9^2)=1 ?
The eccentricity (x^2)/(2^2)+(y^2)/(9^2)=1 is (sqrt(77))/9