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

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

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foci y^2-x^2=4

foci

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

(0, 22), (0, - 22)

Solution steps

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

Calculate Hyperbola properties

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

Up-down Hyperbola with

(h, k) = (0, 0), a = 2, b = 2

(0, 0 + c), (0, 0 - c)

Compute

c :

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

(0, 0 + 22), (0, 0 - 22)

Refine

(0, 22), (0, - 22)

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

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

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

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

\frac{( x - 5 ) ^{2}}{12} - \frac{( y + 6 ) ^{2}}{17} = 1