What is the foci ((y-1)^2)/4-((x+8)^2)/(25)=1 ?

The foci ((y-1)^2)/4-((x+8)^2)/(25)=1 is (-8,1+sqrt(29)),(-8,1-sqrt(29))

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foci ((y-1)^2)/4-((x+8)^2)/(25)=1

foci

\frac{( y - 1 ) ^{2}}{4} - \frac{( x + 8 ) ^{2}}{25} = 1

(- 8, 1 + 29), (- 8, 1 - 29)

Solution steps

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

Calculate Hyperbola properties

\frac{( y - 1 ) ^{2}}{4} - \frac{( x + 8 ) ^{2}}{25} = 1 :

Up-down Hyperbola with

(h, k) = (- 8, 1), a = 2, b = 5

(- 8, 1 + c), (- 8, 1 - c)

Compute

c :

c = 2^{2} + 5^{2} : 29

(- 8, 1 + 29), (- 8, 1 - 29)

\frac{( x - 3 ) ^{2}}{11} - \frac{( y + 1 ) ^{2}}{5} = 1

16 x^{2} - y^{2} - 96 x - 6 y + 119 = 0

9 x^{2} - 18 x - 16 y^{2} - 64 y = 199

18 x^{2} - 32 y^{2} = 2

16 x^{2} - 9 y^{2} - 64 x - 18 y + 199 = 0

What is the foci ((y-1)^2)/4-((x+8)^2)/(25)=1 ?
The foci ((y-1)^2)/4-((x+8)^2)/(25)=1 is (-8,1+sqrt(29)),(-8,1-sqrt(29))