What is the foci (y^2)/(25)-(x^2)/(64)=1 ?

The foci (y^2)/(25)-(x^2)/(64)=1 is (0,sqrt(89)),(0,-sqrt(89))

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foci (y^2)/(25)-(x^2)/(64)=1

foci

\frac{y ^{2}}{25} - \frac{x ^{2}}{64} = 1

(0, 89), (0, - 89)

Solution steps

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

Calculate Hyperbola properties

\frac{y ^{2}}{25} - \frac{x ^{2}}{64} = 1 :

Up-down Hyperbola with

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

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

Compute

c :

c = 5^{2} + 8^{2} : 89

(0, 0 + 89), (0, 0 - 89)

Refine

(0, 89), (0, - 89)

9 y^{2} + 36 y - 4 x^{2} - 32 x - 64 = 0

16 y^{2} + 64 y - x^{2} + 2 x = 1

- x^{2} + 9 y^{2} + 90 y + 189 = 0

\frac{( y - 3 ) ^{2}}{9} - \frac{( x + 1 ) ^{2}}{45} = 1

36 x^{2} - 4 y^{2} - 216 x + 16 y + 452 = 0

What is the foci (y^2)/(25)-(x^2)/(64)=1 ?
The foci (y^2)/(25)-(x^2)/(64)=1 is (0,sqrt(89)),(0,-sqrt(89))