What is the foci 9x^2+16y^2-18x-64y-71=0 ?

The foci 9x^2+16y^2-18x-64y-71=0 is (1+sqrt(7),2),(1-sqrt(7),2)

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foci 9x^2+16y^2-18x-64y-71=0

foci

9 x^{2} + 16 y^{2} - 18 x - 64 y - 71 = 0

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

Solution steps

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

Calculate ellipse properties

9 x^{2} + 16 y^{2} - 18 x - 64 y - 71 = 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}}{16} + \frac{y ^{2}}{5} = 1

81 x^{2} + 16 y^{2} = 1296

25 x^{2} + 9 y^{2} - 100 x - 90 y + 100 = 0

5 x^{2} + 7 y^{2} - 35 = 0

4 (x - 1)^{2} + 13 (y + 3)^{2} = 52

What is the foci 9x^2+16y^2-18x-64y-71=0 ?
The foci 9x^2+16y^2-18x-64y-71=0 is (1+sqrt(7),2),(1-sqrt(7),2)