What is the eccentricity 2x^2+y^2-8y-2x+1=0 ?

The eccentricity 2x^2+y^2-8y-2x+1=0 is 1/(sqrt(2))

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eccentricity 2x^2+y^2-8y-2x+1=0

eccentricity

2 x^{2} + y^{2} - 8 y - 2 x + 1 = 0

\frac{1}{2}

Solution steps

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

Calculate ellipse properties

2 x^{2} + y^{2} - 8 y - 2 x + 1 = 0 :

Ellipse with center

(h, k) = (\frac{1}{2}, 4), b = \frac{31}{2}, a = \frac{31}{2}

= \frac{( \frac{31}{2} ) ^{2} - ( \frac{31}{2} ) ^{2}}{\frac{31}{2}}

\frac{( \frac{31}{2} ) ^{2} - ( \frac{31}{2} ) ^{2}}{\frac{31}{2}} = \frac{1}{2}

= \frac{1}{2}

\frac{x ^{2}}{36} + \frac{y ^{2}}{81} = 1

\frac{1}{5} x^{2} + \frac{1}{125} y^{2} = 5

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

3 x^{2} + 7 y^{2} = 63

\frac{x ^{2}}{160} + \frac{y ^{2}}{16} = 1

What is the eccentricity 2x^2+y^2-8y-2x+1=0 ?
The eccentricity 2x^2+y^2-8y-2x+1=0 is 1/(sqrt(2))