What is the foci ((y+1)^2)/(49)-((x+3)^2)/(64)=1 ?

The foci ((y+1)^2)/(49)-((x+3)^2)/(64)=1 is (-3,-1+sqrt(113)),(-3,-1-sqrt(113))

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foci ((y+1)^2)/(49)-((x+3)^2)/(64)=1

foci

\frac{( y + 1 ) ^{2}}{49} - \frac{( x + 3 ) ^{2}}{64} = 1

(- 3, - 1 + 113), (- 3, - 1 - 113)

Solution steps

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

Calculate Hyperbola properties

\frac{( y + 1 ) ^{2}}{49} - \frac{( x + 3 ) ^{2}}{64} = 1 :

Up-down Hyperbola with

(h, k) = (- 3, - 1), a = 7, b = 8

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

Compute

c :

c = 7^{2} + 8^{2} : 113

(- 3, - 1 + 113), (- 3, - 1 - 113)

289 y^{2} - x^{2} = 1

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

\frac{( x + 2 ) ^{2}}{49} - \frac{( y - 2 ) ^{2}}{45} = 1

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

\frac{x ^{2}}{18} - \frac{y ^{2}}{7} = 1

What is the foci ((y+1)^2)/(49)-((x+3)^2)/(64)=1 ?
The foci ((y+1)^2)/(49)-((x+3)^2)/(64)=1 is (-3,-1+sqrt(113)),(-3,-1-sqrt(113))