What is the foci y^2-x^2=36 ?

The foci y^2-x^2=36 is (0,6sqrt(2)),(0,-6sqrt(2))

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foci y^2-x^2=36

foci

y^{2} - x^{2} = 36

(0, 62), (0, - 62)

Solution steps

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

Calculate Hyperbola properties

y^{2} - x^{2} = 36 :

Up-down Hyperbola with

(h, k) = (0, 0), a = 6, b = 6

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

Compute

c :

c = 6^{2} + 6^{2} : 62

(0, 0 + 62), (0, 0 - 62)

Refine

(0, 62), (0, - 62)

y^{2} - x^{2} = 22

16 x^{2} - 96 x - 9 y^{2} + 36 y - 36 = 0

\frac{x ^{2}}{4} - \frac{y ^{2}}{49} = 1

\frac{( y - 1 ) ^{2}}{4} - \frac{( x + 8 ) ^{2}}{25} = 1

\frac{( x - 3 ) ^{2}}{11} - \frac{( y + 1 ) ^{2}}{5} = 1