What is the foci 4y^2-9x^2+8y-54x-113=0 ?

The foci 4y^2-9x^2+8y-54x-113=0 is (-3,-1+sqrt(13)),(-3,-1-sqrt(13))

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foci 4y^2-9x^2+8y-54x-113=0

foci

4 y^{2} - 9 x^{2} + 8 y - 54 x - 113 = 0

(- 3, - 1 + 13), (- 3, - 1 - 13)

Solution steps

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

Calculate Hyperbola properties

4 y^{2} - 9 x^{2} + 8 y - 54 x - 113 = 0 :

Up-down Hyperbola with

(h, k) = (- 3, - 1), a = 3, b = 2

(- 3, - 1 + c), (- 3, - 1 - c)

Compute

c :

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

(- 3, - 1 + 13), (- 3, - 1 - 13)

9 x^{2} - 4 y^{2} = 1

\frac{( x - 7 ) ^{2}}{100} - \frac{( y + 8 ) ^{2}}{25} = 1

\frac{x ^{2}}{4} - (\frac{y + 1}{16})^{2} = 1

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

x^{2} - 4 y^{2} + 16 y - 32 = 0

What is the foci 4y^2-9x^2+8y-54x-113=0 ?
The foci 4y^2-9x^2+8y-54x-113=0 is (-3,-1+sqrt(13)),(-3,-1-sqrt(13))