What is the foci 25y^2-16x^2-400=0 ?

The foci 25y^2-16x^2-400=0 is (0,sqrt(41)),(0,-sqrt(41))

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foci 25y^2-16x^2-400=0

foci

25 y^{2} - 16 x^{2} - 400 = 0

(0, 41), (0, - 41)

Solution steps

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

Calculate Hyperbola properties

25 y^{2} - 16 x^{2} - 400 = 0 :

Up-down Hyperbola with

(h, k) = (0, 0), a = 4, b = 5

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

Compute

c :

c = 4^{2} + 5^{2} : 41

(0, 0 + 41), (0, 0 - 41)

Refine

(0, 41), (0, - 41)

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

\frac{x ^{2}}{81} - \frac{y ^{2}}{9} = 1

\frac{y ^{2}}{16} - \frac{x ^{2}}{49} = 1

\frac{y ^{2}}{25} - \frac{x ^{2}}{144} = 1

9 y^{2} - x^{2} + 2 x + 54 y + 62 = 0

What is the foci 25y^2-16x^2-400=0 ?
The foci 25y^2-16x^2-400=0 is (0,sqrt(41)),(0,-sqrt(41))