What is the eccentricity x^2+2y^2-2x+8y+5=0 ?

The eccentricity x^2+2y^2-2x+8y+5=0 is 1/(sqrt(2))

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eccentricity x^2+2y^2-2x+8y+5=0

eccentricity

x^{2} + 2 y^{2} - 2 x + 8 y + 5 = 0

\frac{1}{2}

Solution steps

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

Calculate ellipse properties

x^{2} + 2 y^{2} - 2 x + 8 y + 5 = 0 :

Ellipse with center

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

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

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

= \frac{1}{2}

\frac{x ^{2}}{8} + \frac{y ^{2}}{4} = 1

\frac{x ^{2}}{144} + \frac{y ^{2}}{169} = 1

\frac{x ^{2}}{4} + \frac{y ^{2}}{1} = 1

\frac{( x ) ^{2}}{12} + \frac{( y ) ^{2}}{16} = 1

\frac{x ^{2}}{4} + \frac{y ^{2}}{25} = 1

What is the eccentricity x^2+2y^2-2x+8y+5=0 ?
The eccentricity x^2+2y^2-2x+8y+5=0 is 1/(sqrt(2))