What is the eccentricity x^2+4y^2-2x-16y+13=0 ?

The eccentricity x^2+4y^2-2x-16y+13=0 is (sqrt(3))/2

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eccentricity x^2+4y^2-2x-16y+13=0

eccentricity

x^{2} + 4 y^{2} - 2 x - 16 y + 13 = 0

\frac{3}{2}

Solution steps

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

Calculate ellipse properties

x^{2} + 4 y^{2} - 2 x - 16 y + 13 = 0 :

Ellipse with center

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

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

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

= \frac{3}{2}

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

\frac{( x - 1 ) ^{2}}{6} + \frac{( y - 3 ) ^{2}}{2} = 1

25 x^{2} + 9 y^{2} - 100 x + 18 y - 116 = 0

\frac{x ^{2}}{16} + \frac{y ^{2}}{36} = 1

\frac{x ^{2}}{8} + \frac{y ^{2}}{3} = 1

What is the eccentricity x^2+4y^2-2x-16y+13=0 ?
The eccentricity x^2+4y^2-2x-16y+13=0 is (sqrt(3))/2