What is the foci-((x+1)^2)/(25)+((y+5)^2)/(16)=1 ?

The foci-((x+1)^2)/(25)+((y+5)^2)/(16)=1 is (-1,-5+sqrt(41)),(-1,-5-sqrt(41))

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foci-((x+1)^2)/(25)+((y+5)^2)/(16)=1

foci

- \frac{( x + 1 ) ^{2}}{25} + \frac{( y + 5 ) ^{2}}{16} = 1

(- 1, - 5 + 41), (- 1, - 5 - 41)

Solution steps

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

Calculate Hyperbola properties

- \frac{( x + 1 ) ^{2}}{25} + \frac{( y + 5 ) ^{2}}{16} = 1 :

Up-down Hyperbola with

(h, k) = (- 1, - 5), a = 4, b = 5

(- 1, - 5 + c), (- 1, - 5 - c)

Compute

c :

c = 4^{2} + 5^{2} : 41

(- 1, - 5 + 41), (- 1, - 5 - 41)

\frac{( x ^{2} )}{4} - 0.12 y^{2} = 1

9 y^{2} - 16 x^{2} = 81

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

\frac{y ^{2}}{6} - \frac{x ^{2}}{6} = 1

x^{2} - y^{2} - 2 x - 6 y - 12 = 0

What is the foci-((x+1)^2)/(25)+((y+5)^2)/(16)=1 ?
The foci-((x+1)^2)/(25)+((y+5)^2)/(16)=1 is (-1,-5+sqrt(41)),(-1,-5-sqrt(41))