What is the foci 64y^2-36x^2=2304 ?

The foci 64y^2-36x^2=2304 is (0,10),(0,-10)

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foci 64y^2-36x^2=2304

foci

64 y^{2} - 36 x^{2} = 2304

(0, 10), (0, - 10)

Solution steps

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

Calculate Hyperbola properties

64 y^{2} - 36 x^{2} = 2304 :

Up-down Hyperbola with

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

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

Compute

c :

c = 6^{2} + 8^{2} : 10

(0, 0 + 10), (0, 0 - 10)

Refine

(0, 10), (0, - 10)

\frac{x ^{2}}{a ^{2}} - \frac{y ^{2}}{b ^{2}} = 1

4 y^{2} - x^{2} + 2 x + 16 y + 7 = 0

\frac{( y + 6 ) ^{2}}{36} - \frac{( x + 4 ) ^{2}}{48} = 1

9 x^{2} - 4 y^{2} - 54 x - 16 y + 29 = 0

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