What is the foci 16x^2+36y^2+192x-288y+576=0 ?

The foci 16x^2+36y^2+192x-288y+576=0 is (-6+2sqrt(5),4),(-6-2sqrt(5),4)

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foci 16x^2+36y^2+192x-288y+576=0

foci

16 x^{2} + 36 y^{2} + 192 x - 288 y + 576 = 0

(- 6 + 25, 4), (- 6 - 25, 4)

Solution steps

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

Calculate ellipse properties

16 x^{2} + 36 y^{2} + 192 x - 288 y + 576 = 0 :

Ellipse with center

(h, k) = (- 6, 4), a = 6, b = 4

(- 6 + c, 4), (- 6 - c, 4)

Compute

c :

c = 6^{2} - 4^{2} : 25

(- 6 + 25, 4), (- 6 - 25, 4)

4 x^{2} - 8 x + y^{2} + 4 y - 92 = 0

\frac{x ^{2}}{9} + (y - 1)^{2} = 1

\frac{x ^{2}}{8} + \frac{y ^{2}}{24} = 1

\frac{( x - 2 ) ^{2}}{49} + \frac{( y + 1 ) ^{2}}{25} = 1

25 x^{2} + 9 y^{2} + 100 x - 125 = 0

What is the foci 16x^2+36y^2+192x-288y+576=0 ?
The foci 16x^2+36y^2+192x-288y+576=0 is (-6+2sqrt(5),4),(-6-2sqrt(5),4)