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

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

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

foci

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

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

Solution steps

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

Calculate Hyperbola properties

4 x^{2} - 9 y^{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{y ^{2}}{36} - \frac{x ^{2}}{49} = 1

\frac{( x + 2 ) ^{2}}{16} - \frac{( y - 3 ) ^{2}}{25} = 1

\frac{( x - 8 ) ^{2}}{9} - \frac{( y + 3 ) ^{2}}{16} = 1

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

\frac{( x - 3 ) ^{2}}{3} - \frac{( y - 2 ) ^{2}}{4} = 1

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