What is the foci 9x^2-16y^2-108x+64y+116=0 ?

The foci 9x^2-16y^2-108x+64y+116=0 is (11,2),(1,2)

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foci 9x^2-16y^2-108x+64y+116=0

foci

9 x^{2} - 16 y^{2} - 108 x + 64 y + 116 = 0

(11, 2), (1, 2)

Solution steps

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

Calculate Hyperbola properties

9 x^{2} - 16 y^{2} - 108 x + 64 y + 116 = 0 :

Right-left Hyperbola with

(h, k) = (6, 2), a = 4, b = 3

(6 + c, 2), (6 - c, 2)

Compute

c :

c = 4^{2} + 3^{2} : 5

(6 + 5, 2), (6 - 5, 2)

Refine

(11, 2), (1, 2)

y^{2} - x^{2} = \frac{9}{25}

\frac{y ^{2}}{25} - \frac{x ^{2}}{11} = 1

\frac{( y ) ^{2}}{121} - \frac{( x ) ^{2}}{81} = 1

8 x^{2} - 3 y^{2} = 24

\frac{( y ) ^{2}}{40} - \frac{( x ) ^{2}}{81} = 1

What is the foci 9x^2-16y^2-108x+64y+116=0 ?
The foci 9x^2-16y^2-108x+64y+116=0 is (11,2),(1,2)