What is the eccentricity 2x^2+3y^2+4x=1 ?

The eccentricity 2x^2+3y^2+4x=1 is 1/(sqrt(3))

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eccentricity 2x^2+3y^2+4x=1

eccentricity

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

\frac{1}{3}

Solution steps

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

Calculate ellipse properties

2 x^{2} + 3 y^{2} + 4 x = 1 :

Ellipse with center

(h, k) = (- 1, 0), a = \frac{3}{2}, b = 1

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

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

= \frac{1}{3}

2 x^{2} + y^{2} = 10

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

18 x^{2} + 8 y^{2} + 36 x - 32 y - 22 = 0

8 x^{2} + 12 y^{2} = 96

\frac{( x ) ^{2}}{11} + \frac{( y ) ^{2}}{16} = 1

What is the eccentricity 2x^2+3y^2+4x=1 ?
The eccentricity 2x^2+3y^2+4x=1 is 1/(sqrt(3))