What is the foci y^2-x^2=1 ?

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

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foci y^2-x^2=1

foci

y^{2} - x^{2} = 1

(0, 2), (0, - 2)

Solution steps

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

Calculate Hyperbola properties

y^{2} - x^{2} = 1 :

Up-down Hyperbola with

(h, k) = (0, 0), a = 1, b = 1

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

Compute

c :

c = 1^{2} + 1^{2} : 2

(0, 0 + 2), (0, 0 - 2)

Refine

(0, 2), (0, - 2)

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

\frac{( x - 6 ) ^{2}}{8} - \frac{( y - 5 ) ^{2}}{1} = 1

\frac{x ^{2}}{16} - \frac{( y + 5 ) ^{2}}{9} = 1

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

x^{2} - 4 y^{2} - 2 x + 16 y = 20