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

\frac{1}{2}

Decimal

0.70710 \dots

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}

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))