What is the foci 25y^2-81x^2=2025 ?

The foci 25y^2-81x^2=2025 is (0,sqrt(106)),(0,-sqrt(106))

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foci 25y^2-81x^2=2025

foci

25 y^{2} - 81 x^{2} = 2025

(0, 106), (0, - 106)

Solution steps

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

Calculate Hyperbola properties

25 y^{2} - 81 x^{2} = 2025 :

Up-down Hyperbola with

(h, k) = (0, 0), a = 9, b = 5

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

Compute

c :

c = 9^{2} + 5^{2} : 106

(0, 0 + 106), (0, 0 - 106)

Refine

(0, 106), (0, - 106)

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

\frac{( y + 3 ) ^{2}}{64} - \frac{( x + 6 ) ^{2}}{49} = 1

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

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

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

What is the foci 25y^2-81x^2=2025 ?
The foci 25y^2-81x^2=2025 is (0,sqrt(106)),(0,-sqrt(106))