What is the eccentricity ((x-4)^2)/3+(y^2)/9 =1 ?

The eccentricity ((x-4)^2)/3+(y^2)/9 =1 is sqrt(2/3)

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eccentricity ((x-4)^2)/3+(y^2)/9 =1

eccentricity

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

\frac{2}{3}

Solution steps

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

Calculate ellipse properties

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

Ellipse with center

(h, k) = (4, 0), b = 3, a = 3

= \frac{3 ^{2} - ( 3 ) ^{2}}{3}

\frac{3 ^{2} - ( 3 ) ^{2}}{3} = \frac{2}{3}

= \frac{2}{3}

\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

\frac{x ^{2}}{36} + \frac{y ^{2}}{11} = 1

What is the eccentricity ((x-4)^2)/3+(y^2)/9 =1 ?
The eccentricity ((x-4)^2)/3+(y^2)/9 =1 is sqrt(2/3)