What is the foci 25y^2-36(x-8)^2=900 ?

The foci 25y^2-36(x-8)^2=900 is (8,sqrt(61)),(8,-sqrt(61))

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foci 25y^2-36(x-8)^2=900

foci

25 y^{2} - 36 (x - 8)^{2} = 900

(8, 61), (8, - 61)

Solution steps

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

Calculate Hyperbola properties

25 y^{2} - 36 (x - 8)^{2} = 900 :

Up-down Hyperbola with

(h, k) = (8, 0), a = 6, b = 5

(8, 0 + c), (8, 0 - c)

Compute

c :

c = 6^{2} + 5^{2} : 61

(8, 0 + 61), (8, 0 - 61)

Refine

(8, 61), (8, - 61)

\frac{y ^{2}}{16} - \frac{x ^{2}}{36} = 1

4 y^{2} - 9 x^{2} = 36

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

\frac{( y - 2 ) ^{2}}{4} - \frac{( x + 3 ) ^{2}}{9} = 1

16 x^{2} - 20 y^{2} - 320 = 0

What is the foci 25y^2-36(x-8)^2=900 ?
The foci 25y^2-36(x-8)^2=900 is (8,sqrt(61)),(8,-sqrt(61))