What is the eccentricity 4x^2+3y^2+24x+36y+72=0 ?

The eccentricity 4x^2+3y^2+24x+36y+72=0 is 1/2

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eccentricity 4x^2+3y^2+24x+36y+72=0

eccentricity

4 x^{2} + 3 y^{2} + 24 x + 36 y + 72 = 0

\frac{1}{2}

Solution steps

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

Calculate ellipse properties

4 x^{2} + 3 y^{2} + 24 x + 36 y + 72 = 0 :

Ellipse with center

(h, k) = (- 3, - 6), b = 26, a = 32

= \frac{( 2 6 ) ^{2} - ( 3 2 ) ^{2}}{2 6}

\frac{( 2 6 ) ^{2} - ( 3 2 ) ^{2}}{2 6} = \frac{1}{2}

= \frac{1}{2}

\frac{5}{81} x^{2} + \frac{y ^{2}}{9} = 1

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

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

What is the eccentricity 4x^2+3y^2+24x+36y+72=0 ?
The eccentricity 4x^2+3y^2+24x+36y+72=0 is 1/2