What is the eccentricity 4x^2-16x+3y^2+24y+52=0 ?

The eccentricity 4x^2-16x+3y^2+24y+52=0 is 1/2

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

eccentricity

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

\frac{1}{2}

Solution steps

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

Calculate ellipse properties

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

Ellipse with center

(h, k) = (2, - 4), b = 2, a = 3

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

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

= \frac{1}{2}

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

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

3 x^{2} + 2 y^{2} + 6 x - 4 y + 5 = 18

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

3 x^{2} + 6 y^{2} = 18

What is the eccentricity 4x^2-16x+3y^2+24y+52=0 ?
The eccentricity 4x^2-16x+3y^2+24y+52=0 is 1/2