What is the foci 9x^2-9y^2-18x+54=0 ?

The foci 9x^2-9y^2-18x+54=0 is (1,sqrt(10)),(1,-sqrt(10))

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foci 9x^2-9y^2-18x+54=0

foci

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

(1, 10), (1, - 10)

Solution steps

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

Calculate Hyperbola properties

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

Up-down Hyperbola with

(h, k) = (1, 0), a = 5, b = 5

(1, 0 + c), (1, 0 - c)

Compute

c :

c = 5^{2} + 5^{2} : 10

(1, 0 + 10), (1, 0 - 10)

Refine

(1, 10), (1, - 10)

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

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

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

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

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

What is the foci 9x^2-9y^2-18x+54=0 ?
The foci 9x^2-9y^2-18x+54=0 is (1,sqrt(10)),(1,-sqrt(10))