What is the foci 4x^2-12y^2-24x+24y+51=0 ?

The foci 4x^2-12y^2-24x+24y+51=0 is (3,4),(3,-2)

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foci 4x^2-12y^2-24x+24y+51=0

foci

4 x^{2} - 12 y^{2} - 24 x + 24 y + 51 = 0

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

Solution steps

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

Calculate Hyperbola properties

4 x^{2} - 12 y^{2} - 24 x + 24 y + 51 = 0 :

Up-down Hyperbola with

(h, k) = (3, 1), a = \frac{3}{2}, b = \frac{3 3}{2}

(3, 1 + c), (3, 1 - c)

Compute

c :

c = (\frac{3}{2})^{2} + (\frac{3 3}{2})^{2} : 3

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

Refine

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

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

x^{2} - 9 y^{2} - 4 x + 36 y - 41 = 0

4 y^{2} - 9 x^{2} + 40 y - 540 x - 8036 = 0

\frac{x ^{2}}{49} - y^{2} = 1

4 x^{2} - 4 y^{2} + 20 x - 16 y + 25 = 0

What is the foci 4x^2-12y^2-24x+24y+51=0 ?
The foci 4x^2-12y^2-24x+24y+51=0 is (3,4),(3,-2)