What is the foci 16x^2+192x+576+25y^2=1600 ?

The foci 16x^2+192x+576+25y^2=1600 is (0,0),(-12,0)

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foci 16x^2+192x+576+25y^2=1600

foci

16 x^{2} + 192 x + 576 + 25 y^{2} = 1600

(0, 0), (- 12, 0)

Solution steps

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

Calculate ellipse properties

16 x^{2} + 192 x + 576 + 25 y^{2} = 1600 :

Ellipse with center

(h, k) = (- 6, 0), a = 10, b = 8

(- 6 + c, 0), (- 6 - c, 0)

Compute

c :

c = 1 0^{2} - 8^{2} : 6

(- 6 + 6, 0), (- 6 - 6, 0)

Refine

(0, 0), (- 12, 0)

\frac{( x - 2 ) ^{2}}{25} + \frac{( y + 1 ) ^{2}}{9} = 1

\frac{( x + 2 ) ^{2}}{9} + \frac{( y - 2 ) ^{2}}{4} = 1

5 x^{2} + 9 y^{2} + 30 x = 0

\frac{x ^{2}}{64} + \frac{y ^{2}}{9} = 1

\frac{x ^{2}}{20} + \frac{y ^{2}}{36} = 1

What is the foci 16x^2+192x+576+25y^2=1600 ?
The foci 16x^2+192x+576+25y^2=1600 is (0,0),(-12,0)