What is the foci 4x^2-12y^2-16x-72y-44=0 ?

The foci 4x^2-12y^2-16x-72y-44=0 is (2,1),(2,-7)

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foci 4x^2-12y^2-16x-72y-44=0

foci

4 x^{2} - 12 y^{2} - 16 x - 72 y - 44 = 0

(2, 1), (2, - 7)

Solution steps

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

Calculate Hyperbola properties

4 x^{2} - 12 y^{2} - 16 x - 72 y - 44 = 0 :

Up-down Hyperbola with

(h, k) = (2, - 3), a = 2, b = 23

(2, - 3 + c), (2, - 3 - c)

Compute

c :

c = 2^{2} + (23)^{2} : 4

(2, - 3 + 4), (2, - 3 - 4)

Refine

(2, 1), (2, - 7)

- 25 x^{2} + 36 y^{2} = 900

x^{2} - 9 y^{2} = 36

\frac{( y + 5 ) ^{2}}{9} - \frac{( x + 2 ) ^{2}}{16} = 1

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

x^{2} - 16 y^{2} = 144

What is the foci 4x^2-12y^2-16x-72y-44=0 ?
The foci 4x^2-12y^2-16x-72y-44=0 is (2,1),(2,-7)