What is the eccentricity ((x+5)^2)/9+(y-1)^2=1 ?

The eccentricity ((x+5)^2)/9+(y-1)^2=1 is (2sqrt(2))/3

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eccentricity ((x+5)^2)/9+(y-1)^2=1

eccentricity

\frac{( x + 5 ) ^{2}}{9} + (y - 1)^{2} = 1

\frac{2 2}{3}

Solution steps

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

Calculate ellipse properties

\frac{( x + 5 ) ^{2}}{9} + (y - 1)^{2} = 1 :

Ellipse with center

(h, k) = (- 5, 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}

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

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

What is the eccentricity ((x+5)^2)/9+(y-1)^2=1 ?
The eccentricity ((x+5)^2)/9+(y-1)^2=1 is (2sqrt(2))/3