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

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

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

foci

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

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

Solution steps

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

Calculate Hyperbola properties

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

Up-down Hyperbola with

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

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

Compute

c :

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

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

Refine

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

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

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

\frac{x ^{2}}{64} + \frac{y ^{2}}{36} = 1

x^{2} + y^{2} = 6

x^{2} = 16 y

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