What is the foci 6x^2+8y^2+12x-32y=178 ?

The foci 6x^2+8y^2+12x-32y=178 is (2,2),(-4,2)

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foci 6x^2+8y^2+12x-32y=178

foci

6 x^{2} + 8 y^{2} + 12 x - 32 y = 178

(2, 2), (- 4, 2)

Solution steps

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

Calculate ellipse properties

6 x^{2} + 8 y^{2} + 12 x - 32 y = 178 :

Ellipse with center

(h, k) = (- 1, 2), a = 6, b = 33

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

Compute

c :

c = 6^{2} - (33)^{2} : 3

(- 1 + 3, 2), (- 1 - 3, 2)

Refine

(2, 2), (- 4, 2)

9 x^{2} + 49 y^{2} - 144 x + 490 y + 1360 = 0

9 x^{2} + 18 x + 4 y^{2} - 24 y + 9 = 0

x^{2} + 4 y^{2} - 6 x + 20 y - 2 = 0

\frac{( x + 2 ) ^{2}}{9} + \frac{( y - 1 ) ^{2}}{16} = 1

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

What is the foci 6x^2+8y^2+12x-32y=178 ?
The foci 6x^2+8y^2+12x-32y=178 is (2,2),(-4,2)