What is the eccentricity 3x^2+y^2-24x+39=0 ?

The eccentricity 3x^2+y^2-24x+39=0 is sqrt(2/3)

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eccentricity 3x^2+y^2-24x+39=0

eccentricity

3 x^{2} + y^{2} - 24 x + 39 = 0

\frac{2}{3}

Solution steps

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

Calculate ellipse properties

3 x^{2} + y^{2} - 24 x + 39 = 0 :

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} + 16 y^{2} = 144

4 x^{2} + y^{2} + 8 x - 4 y + 4 = 0

4 x^{2} - 16 x + 3 y^{2} + 24 y + 52 = 0

x^{2} + 8 y^{2} = 32

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

What is the eccentricity 3x^2+y^2-24x+39=0 ?
The eccentricity 3x^2+y^2-24x+39=0 is sqrt(2/3)