What is the eccentricity 4x^2+3y^2-8x+18y+19=0 ?

The eccentricity 4x^2+3y^2-8x+18y+19=0 is 1/2

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eccentricity 4x^2+3y^2-8x+18y+19=0

eccentricity

4 x^{2} + 3 y^{2} - 8 x + 18 y + 19 = 0

\frac{1}{2}

Solution steps

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

Calculate ellipse properties

4 x^{2} + 3 y^{2} - 8 x + 18 y + 19 = 0 :

Ellipse with center

(h, k) = (1, - 3), b = 2, a = 3

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

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

= \frac{1}{2}

x^{2} + 4 y^{2} - 6 x + 20 y - 2 = 0

\frac{x ^{2}}{25} + \frac{( y + 3 ) ^{2}}{49} = 1

36 x^{2} + 9 y^{2} + 36 y - 288 = 0

9 x^{2} + 4 y^{2} - 54 x + 32 y + 1 = 0

16 x^{2} + 25 y^{2} - 96 x + 100 y - 156 = 0

What is the eccentricity 4x^2+3y^2-8x+18y+19=0 ?
The eccentricity 4x^2+3y^2-8x+18y+19=0 is 1/2