What is the foci 4x^2+36y^2+24x+432y=-1188 ?

The foci 4x^2+36y^2+24x+432y=-1188 is (-3+4sqrt(2),-6),(-3-4sqrt(2),-6)

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foci 4x^2+36y^2+24x+432y=-1188

foci

4 x^{2} + 36 y^{2} + 24 x + 432 y = - 1188

(- 3 + 42, - 6), (- 3 - 42, - 6)

Solution steps

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

Calculate ellipse properties

4 x^{2} + 36 y^{2} + 24 x + 432 y = - 1188 :

Ellipse with center

(h, k) = (- 3, - 6), a = 6, b = 2

(- 3 + c, - 6), (- 3 - c, - 6)

Compute

c :

c = 6^{2} - 2^{2} : 42

(- 3 + 42, - 6), (- 3 - 42, - 6)

\frac{( x - 2 ) ^{2}}{16} + \frac{( y + 3 ) ^{2}}{9} = 1

\frac{x ^{2}}{25} + \frac{y ^{2}}{169} = 1

16 x^{2} - 96 x + 9 y^{2} = 0

x^{2} + 4 y^{2} - 6 x - 16 y + 21 = 0

81 x^{2} - 1296 x + 16 y^{2} + 64 y = - 3952

What is the foci 4x^2+36y^2+24x+432y=-1188 ?
The foci 4x^2+36y^2+24x+432y=-1188 is (-3+4sqrt(2),-6),(-3-4sqrt(2),-6)