What is the foci 9y^2+36y-4x^2-32x-64=0 ?

The foci 9y^2+36y-4x^2-32x-64=0 is (-4,-2+sqrt(13)),(-4,-2-sqrt(13))

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

foci

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

(- 4, - 2 + 13), (- 4, - 2 - 13)

Solution steps

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

Calculate Hyperbola properties

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

Up-down Hyperbola with

(h, k) = (- 4, - 2), a = 2, b = 3

(- 4, - 2 + c), (- 4, - 2 - c)

Compute

c :

c = 2^{2} + 3^{2} : 13

(- 4, - 2 + 13), (- 4, - 2 - 13)

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

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

What is the foci 9y^2+36y-4x^2-32x-64=0 ?
The foci 9y^2+36y-4x^2-32x-64=0 is (-4,-2+sqrt(13)),(-4,-2-sqrt(13))