What is the foci x^2-2x-3=y^2+2y+3 ?

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

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foci x^2-2x-3=y^2+2y+3

foci

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

(1 + 23, - 1), (1 - 23, - 1)

Solution steps

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

Calculate Hyperbola properties

x^{2} - 2 x - 3 = y^{2} + 2 y + 3 :

Right-left Hyperbola with

(h, k) = (1, - 1), a = 6, b = 6

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

Compute

c :

c = 6^{2} + 6^{2} : 23

(1 + 23, - 1), (1 - 23, - 1)

6 x^{2} - 5 y^{2} - 24 x + 10 y - 11 = 0

4 x^{2} - 24 x - 25 y^{2} + 250 y - 489 = 0

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

9 y^{2} - 4 x^{2} + 32 x - 36 y - 64 = 0

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

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