What is the foci y^2-x^2=25 ?

The foci y^2-x^2=25 is (0,5sqrt(2)),(0,-5sqrt(2))

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foci y^2-x^2=25

foci

y^{2} - x^{2} = 25

(0, 52), (0, - 52)

Solution steps

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

Calculate Hyperbola properties

y^{2} - x^{2} = 25 :

Up-down Hyperbola with

(h, k) = (0, 0), a = 5, b = 5

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

Compute

c :

c = 5^{2} + 5^{2} : 52

(0, 0 + 52), (0, 0 - 52)

Refine

(0, 52), (0, - 52)

\frac{x ^{2}}{140} - \frac{( y - 6 ) ^{2}}{4} = - 1

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

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

\frac{y ^{2}}{25} - x^{2} = 1

\frac{x ^{2}}{16} - \frac{y ^{2}}{48} = 1