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

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

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

foci

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

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

Solution steps

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

Calculate Hyperbola properties

9 y^{2} - 4 x^{2} + 32 x - 36 y - 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)

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

x^{2} + 6 x = 9 y^{2}

\frac{x ^{2}}{140} - \frac{( y - 6 ) ^{2}}{4} = 1

\frac{x ^{2}}{9} - \frac{y ^{2}}{36} = 1

\frac{x ^{2}}{4} - \frac{( y - 6 ) ^{2}}{140} = 1

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