What is the eccentricity 18x^2+4y^2-72x+4y+37=0 ?

The eccentricity 18x^2+4y^2-72x+4y+37=0 is (sqrt(7))/3

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eccentricity 18x^2+4y^2-72x+4y+37=0

eccentricity

18 x^{2} + 4 y^{2} - 72 x + 4 y + 37 = 0

\frac{7}{3}

Solution steps

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

Calculate ellipse properties

18 x^{2} + 4 y^{2} - 72 x + 4 y + 37 = 0 :

Ellipse with center

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

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

\frac{3 ^{2} - ( 2 ) ^{2}}{3} = \frac{7}{3}

= \frac{7}{3}

\frac{x ^{2}}{9} + y^{2} = 1

\frac{x ^{2}}{12} + \frac{y ^{2}}{49} = 1

\frac{x ^{2}}{4} + \frac{y ^{2}}{3} = 1

\frac{x ^{2}}{169} + \frac{y ^{2}}{25} = 1

16 x^{2} + 9 y^{2} + 160 x - 72 y + 544 = 144

What is the eccentricity 18x^2+4y^2-72x+4y+37=0 ?
The eccentricity 18x^2+4y^2-72x+4y+37=0 is (sqrt(7))/3