What is the foci 9x^2-y^2-54x-2y+71=0 ?

The foci 9x^2-y^2-54x-2y+71=0 is (3+sqrt(10),-1),(3-sqrt(10),-1)

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foci 9x^2-y^2-54x-2y+71=0

foci

9 x^{2} - y^{2} - 54 x - 2 y + 71 = 0

(3 + 10, - 1), (3 - 10, - 1)

Solution steps

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

Calculate Hyperbola properties

9 x^{2} - y^{2} - 54 x - 2 y + 71 = 0 :

Right-left Hyperbola with

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

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

Compute

c :

c = 1^{2} + 3^{2} : 10

(3 + 10, - 1), (3 - 10, - 1)

25 x^{2} + 56476 x - 25 y^{2} - 3 y = 48838

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

10 x^{2} - 25 y^{2} = 100

\frac{x ^{2}}{4} - \frac{y ^{2}}{1} = 1

12 x^{2} - 3 y^{2} = 36

What is the foci 9x^2-y^2-54x-2y+71=0 ?
The foci 9x^2-y^2-54x-2y+71=0 is (3+sqrt(10),-1),(3-sqrt(10),-1)