What is the foci 9x^2-4y^2-54x-8y+113=0 ?

The foci 9x^2-4y^2-54x-8y+113=0 is (3,-1+sqrt(13)),(3,-1-sqrt(13))

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foci 9x^2-4y^2-54x-8y+113=0

foci

9 x^{2} - 4 y^{2} - 54 x - 8 y + 113 = 0

(3, - 1 + 13), (3, - 1 - 13)

Solution steps

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

Calculate Hyperbola properties

9 x^{2} - 4 y^{2} - 54 x - 8 y + 113 = 0 :

Up-down Hyperbola with

(h, k) = (3, - 1), a = 3, b = 2

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

Compute

c :

c = 3^{2} + 2^{2} : 13

(3, - 1 + 13), (3, - 1 - 13)

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

x^{2} - 3 y^{2} + 12 = 0

9 x^{2} - 9 y^{2} - 18 x + 54 = 0

25 y^{2} - 9 x^{2} = 225

\frac{y ^{2}}{36} - \frac{x ^{2}}{81} = 1

What is the foci 9x^2-4y^2-54x-8y+113=0 ?
The foci 9x^2-4y^2-54x-8y+113=0 is (3,-1+sqrt(13)),(3,-1-sqrt(13))