What is the foci 4x^2+9y^2-48x+72y=-144 ?

The foci 4x^2+9y^2-48x+72y=-144 is (6+2sqrt(5),-4),(6-2sqrt(5),-4)

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foci 4x^2+9y^2-48x+72y=-144

foci

4 x^{2} + 9 y^{2} - 48 x + 72 y = - 144

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

Solution steps

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

Calculate ellipse properties

4 x^{2} + 9 y^{2} - 48 x + 72 y = - 144 :

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)

36 x^{2} + 16 y^{2} - 180 x + 96 y - 207 = 0

x^{2} + 2 y^{2} + 2 x - 4 y - 1 = 0

2 x^{2} + 3 y^{2} = 6

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

\frac{x ^{2}}{16} + \frac{( y - 1 ) ^{2}}{36} = 1

What is the foci 4x^2+9y^2-48x+72y=-144 ?
The foci 4x^2+9y^2-48x+72y=-144 is (6+2sqrt(5),-4),(6-2sqrt(5),-4)