What is the foci 16x^2-y^2-96x-6y+119=0 ?

The foci 16x^2-y^2-96x-6y+119=0 is (3+sqrt(17),-3),(3-sqrt(17),-3)

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foci 16x^2-y^2-96x-6y+119=0

foci

16 x^{2} - y^{2} - 96 x - 6 y + 119 = 0

(3 + 17, - 3), (3 - 17, - 3)

Solution steps

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

Calculate Hyperbola properties

16 x^{2} - y^{2} - 96 x - 6 y + 119 = 0 :

Right-left Hyperbola with

(h, k) = (3, - 3), a = 1, b = 4

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

Compute

c :

c = 1^{2} + 4^{2} : 17

(3 + 17, - 3), (3 - 17, - 3)

9 x^{2} - 18 x - 16 y^{2} - 64 y = 199

18 x^{2} - 32 y^{2} = 2

16 x^{2} - 9 y^{2} - 64 x - 18 y + 199 = 0

\frac{x ^{2}}{144} - \frac{y ^{2}}{81} = 1

\frac{y ^{2}}{25} - \frac{x ^{2}}{49} = 1

What is the foci 16x^2-y^2-96x-6y+119=0 ?
The foci 16x^2-y^2-96x-6y+119=0 is (3+sqrt(17),-3),(3-sqrt(17),-3)