What is the eccentricity 3x^2+2y^2-12x+8y+19=0 ?

The eccentricity 3x^2+2y^2-12x+8y+19=0 is 1/(sqrt(3))

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eccentricity 3x^2+2y^2-12x+8y+19=0

eccentricity

3 x^{2} + 2 y^{2} - 12 x + 8 y + 19 = 0

\frac{1}{3}

Solution steps

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

Calculate ellipse properties

3 x^{2} + 2 y^{2} - 12 x + 8 y + 19 = 0 :

Ellipse with center

(h, k) = (2, - 2), b = \frac{1}{2}, a = \frac{1}{3}

= \frac{( \frac{1}{2} ) ^{2} - ( \frac{1}{3} ) ^{2}}{\frac{1}{2}}

\frac{( \frac{1}{2} ) ^{2} - ( \frac{1}{3} ) ^{2}}{\frac{1}{2}} = \frac{1}{3}

= \frac{1}{3}

\frac{x ^{2}}{196} + \frac{y ^{2}}{121} = 1

\frac{x ^{2}}{5} + \frac{y ^{2}}{20.98} = 1

16 x^{2} + 192 x + 576 + 25 y^{2} = 1600

x^{2} + y^{2} = 1

x^{2} + 2 y^{2} = 3

What is the eccentricity 3x^2+2y^2-12x+8y+19=0 ?
The eccentricity 3x^2+2y^2-12x+8y+19=0 is 1/(sqrt(3))