What is the eccentricity 3x^2+y^2-24x=-39 ?

The eccentricity 3x^2+y^2-24x=-39 is sqrt(2/3)

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eccentricity 3x^2+y^2-24x=-39

eccentricity

3 x^{2} + y^{2} - 24 x = - 39

\frac{2}{3}

Solution steps

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

Calculate ellipse properties

3 x^{2} + y^{2} - 24 x = - 39 :

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}

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

16 x^{2} + 80 y^{2} = 1280

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

4 x^{2} + 9 y^{2} = 13

4 - x^{2} - 4 y^{2} > 0

What is the eccentricity 3x^2+y^2-24x=-39 ?
The eccentricity 3x^2+y^2-24x=-39 is sqrt(2/3)