What is the foci 9x^2+16y^2+64y-80=0 ?

The foci 9x^2+16y^2+64y-80=0 is (sqrt(7),-2),(-sqrt(7),-2)

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foci 9x^2+16y^2+64y-80=0

foci

9 x^{2} + 16 y^{2} + 64 y - 80 = 0

(7, - 2), (- 7, - 2)

Solution steps

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

Calculate ellipse properties

9 x^{2} + 16 y^{2} + 64 y - 80 = 0 :

Ellipse with center

(h, k) = (0, - 2), a = 4, b = 3

(0 + c, - 2), (0 - c, - 2)

Compute

c :

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

(0 + 7, - 2), (0 - 7, - 2)

Refine

(7, - 2), (- 7, - 2)

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

9 x^{2} + 9 y^{2} + 18 x - 18 y + 14 = 0

\frac{x ^{2}}{81} + \frac{y ^{2}}{64} = 1

\frac{( x - 2 ) ^{2}}{16} + \frac{( y + 1 ) ^{2}}{25} = 1

36 x^{2} + 9 y^{2} + 48 x - 36 y + 43 = 0

What is the foci 9x^2+16y^2+64y-80=0 ?
The foci 9x^2+16y^2+64y-80=0 is (sqrt(7),-2),(-sqrt(7),-2)