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

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

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

foci

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

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

Solution steps

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

Calculate Hyperbola properties

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

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 ^{2}}{9} - \frac{y ^{2}}{49} = 1

4 x^{2} - 3 y^{2} - 8 x - 8 = 0

\frac{( x - 3 ) ^{2}}{25} - \frac{( y + 1 ) ^{2}}{25} = 1

\frac{x ^{2}}{5625} - \frac{y ^{2}}{1600} = 1

\frac{( y - 6 ) ^{2}}{36} - \frac{( x + 1 ) ^{2}}{16} = 1

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