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

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

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foci x^2-6x-6=y^2+6y+6

foci

x^{2} - 6 x - 6 = y^{2} + 6 y + 6

(3 + 26, - 3), (3 - 26, - 3)

Solution steps

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

Calculate Hyperbola properties

x^{2} - 6 x - 6 = y^{2} + 6 y + 6 :

Right-left Hyperbola with

(h, k) = (3, - 3), a = 23, b = 23

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

Compute

c :

c = (23)^{2} + (23)^{2} : 26

(3 + 26, - 3), (3 - 26, - 3)

\frac{( x + 4 ) ^{2}}{9} - \frac{( y + 3 ) ^{2}}{16} = 1

- 4 y^{2} + 9 x^{2} - 27 x - 16 y = 2

\frac{x ^{2}}{4 ^{2}} - \frac{y ^{2}}{3 ^{2}} = 1

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

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

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