What is the eccentricity 27x^2+48y^2-54x-192y-213=0 ?

The eccentricity 27x^2+48y^2-54x-192y-213=0 is (sqrt(7))/4

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eccentricity 27x^2+48y^2-54x-192y-213=0

eccentricity

27 x^{2} + 48 y^{2} - 54 x - 192 y - 213 = 0

\frac{7}{4}

Solution steps

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

Calculate ellipse properties

27 x^{2} + 48 y^{2} - 54 x - 192 y - 213 = 0 :

Ellipse with center

(h, k) = (1, 2), a = 4, b = 3

= \frac{4 ^{2} - 3 ^{2}}{4}

\frac{4 ^{2} - 3 ^{2}}{4} = \frac{7}{4}

= \frac{7}{4}

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

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

8 x^{2} + 2 y^{2} = 16

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

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

What is the eccentricity 27x^2+48y^2-54x-192y-213=0 ?
The eccentricity 27x^2+48y^2-54x-192y-213=0 is (sqrt(7))/4