What is the foci 25y^2-64x^2=1600 ?

The foci 25y^2-64x^2=1600 is (0,sqrt(89)),(0,-sqrt(89))

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foci 25y^2-64x^2=1600

foci

25 y^{2} - 64 x^{2} = 1600

(0, 89), (0, - 89)

Solution steps

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

Calculate Hyperbola properties

25 y^{2} - 64 x^{2} = 1600 :

Up-down Hyperbola with

(h, k) = (0, 0), a = 8, b = 5

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

Compute

c :

c = 8^{2} + 5^{2} : 89

(0, 0 + 89), (0, 0 - 89)

Refine

(0, 89), (0, - 89)

4 y^{2} - 16 x^{2} = 64

y^{2} - 9 x^{2} - 36 x - 8 y - 29 = 0

x^{2} - y^{2} - 4 x - 2 y - 13 = 0

\frac{( x - 3 ) ^{2}}{9} - \frac{( y - 2 ) ^{2}}{22} = 1

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

What is the foci 25y^2-64x^2=1600 ?
The foci 25y^2-64x^2=1600 is (0,sqrt(89)),(0,-sqrt(89))