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

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

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

eccentricity

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

\frac{1}{2}

Solution steps

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

Calculate ellipse properties

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

Ellipse with center

(h, k) = (0, 1), a = 2, b = 1

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

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

= \frac{1}{2}

\frac{( x + 5 ) ^{2}}{9} + (y - 1)^{2} = 1

36 x^{2} + 5 y^{2} - 90 y - 495 = 0

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

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

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

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