What is the foci x^2-y^2-10x-10y-1=0 ?

The foci x^2-y^2-10x-10y-1=0 is (5+sqrt(2),-5),(5-sqrt(2),-5)

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foci x^2-y^2-10x-10y-1=0

foci

x^{2} - y^{2} - 10 x - 10 y - 1 = 0

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

Solution steps

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

Calculate Hyperbola properties

x^{2} - y^{2} - 10 x - 10 y - 1 = 0 :

Right-left Hyperbola with

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

(5 + c, - 5), (5 - c, - 5)

Compute

c :

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

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

\frac{( x - 3 ) ^{2}}{16} - \frac{( y + 8 ) ^{2}}{64} = 1

9 x^{2} - 4 y^{2} - 18 x - 16 y + 29 = 0

9 y^{2} + 36 y - 4 x^{2} - 24 x - 36 = 0

4 (x - 3)^{2} - 9 (y - 2)^{2} = 36

9 x^{2} - y^{2} - 36 x - 4 y + 23 = 0

What is the foci x^2-y^2-10x-10y-1=0 ?
The foci x^2-y^2-10x-10y-1=0 is (5+sqrt(2),-5),(5-sqrt(2),-5)