What is the foci ((y+3)^2)/(64)-((x+6)^2)/(49)=1 ?

The foci ((y+3)^2)/(64)-((x+6)^2)/(49)=1 is (-6,-3+sqrt(113)),(-6,-3-sqrt(113))

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foci ((y+3)^2)/(64)-((x+6)^2)/(49)=1

foci

\frac{( y + 3 ) ^{2}}{64} - \frac{( x + 6 ) ^{2}}{49} = 1

(- 6, - 3 + 113), (- 6, - 3 - 113)

Solution steps

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

Calculate Hyperbola properties

\frac{( y + 3 ) ^{2}}{64} - \frac{( x + 6 ) ^{2}}{49} = 1 :

Up-down Hyperbola with

(h, k) = (- 6, - 3), a = 8, b = 7

(- 6, - 3 + c), (- 6, - 3 - c)

Compute

c :

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

(- 6, - 3 + 113), (- 6, - 3 - 113)

\frac{( x + 4 ) ^{2}}{4} - \frac{( y - 1 ) ^{2}}{9} = 1

\frac{x ^{2}}{16} - \frac{y ^{2}}{49} = 1

x^{2} - 6 x - 6 = y^{2} + 6 y + 6

\frac{( x + 4 ) ^{2}}{9} - \frac{( y + 3 ) ^{2}}{16} = 1

- 4 y^{2} + 9 x^{2} - 27 x - 16 y = 2

What is the foci ((y+3)^2)/(64)-((x+6)^2)/(49)=1 ?
The foci ((y+3)^2)/(64)-((x+6)^2)/(49)=1 is (-6,-3+sqrt(113)),(-6,-3-sqrt(113))