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

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

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

eccentricity

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

\frac{3}{2}

Solution steps

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

Calculate ellipse properties

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

Ellipse with center

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

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

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

= \frac{3}{2}

\frac{x ^{2}}{6} + \frac{y ^{2}}{12} = 1

\frac{( x - 8 ) ^{2}}{9} + \frac{( y - 3 ) ^{2}}{4} = 1

9 x^{2} + 16 y^{2} - 18 x - 64 y - 71 = 0

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

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

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