What is the foci x^2-y^2-4x-2y-1=0 ?

The foci x^2-y^2-4x-2y-1=0 is (2+2sqrt(2),-1),(2-2sqrt(2),-1)

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foci x^2-y^2-4x-2y-1=0

foci

x^{2} - y^{2} - 4 x - 2 y - 1 = 0

(2 + 22, - 1), (2 - 22, - 1)

Solution steps

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

Calculate Hyperbola properties

x^{2} - y^{2} - 4 x - 2 y - 1 = 0 :

Right-left Hyperbola with

(h, k) = (2, - 1), a = 2, b = 2

(2 + c, - 1), (2 - c, - 1)

Compute

c :

c = 2^{2} + 2^{2} : 22

(2 + 22, - 1), (2 - 22, - 1)

9 x^{2} - y^{2} - 54 x + 45 = 0

x^{2} - 16 y^{2} = 16

3 x^{2} - y^{2} = 11

\frac{y ^{2}}{1 2 ^{2}} - \frac{x ^{2}}{5 ^{2}} = 1

y^{2} - 4 x^{2} - 10 y - 40 x - 100 = 0

What is the foci x^2-y^2-4x-2y-1=0 ?
The foci x^2-y^2-4x-2y-1=0 is (2+2sqrt(2),-1),(2-2sqrt(2),-1)