What is the foci 9y^2+36y-4x^2-24x-36=0 ?

The foci 9y^2+36y-4x^2-24x-36=0 is (-3,-2+sqrt(13)),(-3,-2-sqrt(13))

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foci 9y^2+36y-4x^2-24x-36=0

foci

9 y^{2} + 36 y - 4 x^{2} - 24 x - 36 = 0

(- 3, - 2 + 13), (- 3, - 2 - 13)

Solution steps

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

Calculate Hyperbola properties

9 y^{2} + 36 y - 4 x^{2} - 24 x - 36 = 0 :

Up-down Hyperbola with

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

(- 3, - 2 + c), (- 3, - 2 - c)

Compute

c :

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

(- 3, - 2 + 13), (- 3, - 2 - 13)

4 (x - 3)^{2} - 9 (y - 2)^{2} = 36

9 x^{2} - y^{2} - 36 x - 4 y + 23 = 0

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

\frac{( y - 1 ) ^{2}}{9} - \frac{( x + 3 ) ^{2}}{16} = 1

81 x^{2} + 972 x - 16 y^{2} - 128 y + 1364 = 0

What is the foci 9y^2+36y-4x^2-24x-36=0 ?
The foci 9y^2+36y-4x^2-24x-36=0 is (-3,-2+sqrt(13)),(-3,-2-sqrt(13))