What is the foci 9x^2-y^2-54x-2y-1=0 ?

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

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foci 9x^2-y^2-54x-2y-1=0

foci

9 x^{2} - y^{2} - 54 x - 2 y - 1 = 0

(3 + 310, - 1), (3 - 310, - 1)

Solution steps

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

Calculate Hyperbola properties

9 x^{2} - y^{2} - 54 x - 2 y - 1 = 0 :

Right-left Hyperbola with

(h, k) = (3, - 1), a = 3, b = 9

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

Compute

c :

c = 3^{2} + 9^{2} : 310

(3 + 310, - 1), (3 - 310, - 1)

\frac{x ^{2}}{60} - \frac{y ^{2}}{40} = 1

\frac{( y + 2 ) ^{2}}{9} - \frac{( x - 1 ) ^{2}}{64} = 1

\frac{x ^{2}}{37} - \frac{y ^{2}}{63} = 1

3 x^{2} - y^{2} = 300

4 x^{2} - y^{2} = 4

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