What is the eccentricity x^2+4y^2-6x-16y+21=0 ?

The eccentricity x^2+4y^2-6x-16y+21=0 is (sqrt(3))/2

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eccentricity x^2+4y^2-6x-16y+21=0

eccentricity

x^{2} + 4 y^{2} - 6 x - 16 y + 21 = 0

\frac{3}{2}

Solution steps

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

Calculate ellipse properties

x^{2} + 4 y^{2} - 6 x - 16 y + 21 = 0 :

Ellipse with center

(h, k) = (3, 2), a = 2, b = 1

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

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

= \frac{3}{2}

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

x^{2} + 3 y^{2} = 1

\frac{x ^{2}}{9} + \frac{y ^{2}}{16} > 1

\frac{x ^{2}}{64} + \frac{y ^{2}}{100} = 1

\frac{x ^{2}}{100} + \frac{y ^{2}}{64} = 1

What is the eccentricity x^2+4y^2-6x-16y+21=0 ?
The eccentricity x^2+4y^2-6x-16y+21=0 is (sqrt(3))/2