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

The foci 27x^2+48y^2-54x-192y-213=0 is (1+sqrt(7),2),(1-sqrt(7),2)

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

foci

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

(1 + 7, 2), (1 - 7, 2)

Solution steps

(h + c, k), (h - c, k)

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

(1 + c, 2), (1 - c, 2)

Compute

c :

c = 4^{2} - 3^{2} : 7

(1 + 7, 2), (1 - 7, 2)

\frac{x ^{2}}{46} + \frac{( y + 8 ) ^{2}}{26} = 1

2 x^{2} + 3 y^{2} + 4 x - 6 y - 1 = 0

\frac{x ^{2}}{15} + \frac{( y - 5 ) ^{2}}{20} = 1

x^{2} + 9 y^{2} - 8 x + 18 y - 11 = 0

4 x^{2} + 36 y^{2} - 24 x - 288 y + 611 = 0

What is the foci 27x^2+48y^2-54x-192y-213=0 ?
The foci 27x^2+48y^2-54x-192y-213=0 is (1+sqrt(7),2),(1-sqrt(7),2)