What is the foci x^2-y^2-4x-2y-13=0 ?

The foci x^2-y^2-4x-2y-13=0 is (2+4sqrt(2),-1),(2-4sqrt(2),-1)

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foci x^2-y^2-4x-2y-13=0

foci

x^{2} - y^{2} - 4 x - 2 y - 13 = 0

(2 + 42, - 1), (2 - 42, - 1)

Solution steps

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

Calculate Hyperbola properties

x^{2} - y^{2} - 4 x - 2 y - 13 = 0 :

Right-left Hyperbola with

(h, k) = (2, - 1), a = 4, b = 4

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

Compute

c :

c = 4^{2} + 4^{2} : 42

(2 + 42, - 1), (2 - 42, - 1)

\frac{( x - 3 ) ^{2}}{9} - \frac{( y - 2 ) ^{2}}{22} = 1

\frac{x ^{2}}{16 + ( y - 4 ) ^{2}} = 1

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

\frac{( y + \frac{9}{2} ) ^{2}}{25} - \frac{( x - \frac{7}{2} ) ^{2}}{25} = 1

\frac{( x + 2 ) ^{2}}{9} - \frac{( y - 1 ) ^{2}}{169} = 1

What is the foci x^2-y^2-4x-2y-13=0 ?
The foci x^2-y^2-4x-2y-13=0 is (2+4sqrt(2),-1),(2-4sqrt(2),-1)