What is the foci x^2-y^2-2x-6y-12=0 ?

The foci x^2-y^2-2x-6y-12=0 is (1+2sqrt(2),-3),(1-2sqrt(2),-3)

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foci x^2-y^2-2x-6y-12=0

foci

x^{2} - y^{2} - 2 x - 6 y - 12 = 0

(1 + 22, - 3), (1 - 22, - 3)

Solution steps

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

Calculate Hyperbola properties

x^{2} - y^{2} - 2 x - 6 y - 12 = 0 :

Right-left Hyperbola with

(h, k) = (1, - 3), a = 2, b = 2

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

Compute

c :

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

(1 + 22, - 3), (1 - 22, - 3)

- \frac{x ^{2}}{16} + \frac{y ^{2}}{9} = 1

4 x^{2} - 9 y^{2} = 144

\frac{( y - \frac{9}{2} ) ^{2}}{49} - \frac{( x - \frac{7}{2} ) ^{2}}{49} = 1

9 x^{2} - 4 y^{2} + 18 x - 27 = 0

\frac{x ^{2}}{8} - \frac{y ^{2}}{8} = 1

What is the foci x^2-y^2-2x-6y-12=0 ?
The foci x^2-y^2-2x-6y-12=0 is (1+2sqrt(2),-3),(1-2sqrt(2),-3)