What is the foci ((y-(-2))^2)/9-((x-5)^2)/(27)=1 ?

The foci ((y-(-2))^2)/9-((x-5)^2)/(27)=1 is (5,4),(5,-8)

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foci ((y-(-2))^2)/9-((x-5)^2)/(27)=1

foci

\frac{( y - ( - 2 ) ) ^{2}}{9} - \frac{( x - 5 ) ^{2}}{27} = 1

(5, 4), (5, - 8)

Solution steps

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

Calculate Hyperbola properties

\frac{( y - ( - 2 ) ) ^{2}}{9} - \frac{( x - 5 ) ^{2}}{27} = 1 :

Up-down Hyperbola with

(h, k) = (5, - 2), a = 3, b = 33

(5, - 2 + c), (5, - 2 - c)

Compute

c :

c = 3^{2} + (33)^{2} : 6

(5, - 2 + 6), (5, - 2 - 6)

Refine

(5, 4), (5, - 8)

\frac{( y - 0 ) ^{2}}{1 ^{2}} - \frac{( 3 x - 0 ) ^{2}}{90} = 1

- \frac{x ^{2}}{25} + \frac{y ^{2}}{36} = 1

\frac{( x - 5 ) ^{2}}{4} - \frac{( y + 3 ) ^{2}}{16} = 1

\frac{( x - 0 ) ^{2}}{16} - \frac{( y - 0 ) ^{2}}{9} = 1

\frac{( x - 4 ) ^{2}}{49} - \frac{( y + 6 ) ^{2}}{9} = 1

What is the foci ((y-(-2))^2)/9-((x-5)^2)/(27)=1 ?
The foci ((y-(-2))^2)/9-((x-5)^2)/(27)=1 is (5,4),(5,-8)