What is the foci ((y-3)^2)/9-((x+1)^2)/(45)=1 ?

The foci ((y-3)^2)/9-((x+1)^2)/(45)=1 is (-1,3+3sqrt(6)),(-1,3-3sqrt(6))

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foci ((y-3)^2)/9-((x+1)^2)/(45)=1

foci

\frac{( y - 3 ) ^{2}}{9} - \frac{( x + 1 ) ^{2}}{45} = 1

(- 1, 3 + 36), (- 1, 3 - 36)

Solution steps

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

Calculate Hyperbola properties

\frac{( y - 3 ) ^{2}}{9} - \frac{( x + 1 ) ^{2}}{45} = 1 :

Up-down Hyperbola with

(h, k) = (- 1, 3), a = 3, b = 35

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

Compute

c :

c = 3^{2} + (35)^{2} : 36

(- 1, 3 + 36), (- 1, 3 - 36)

36 x^{2} - 4 y^{2} - 216 x + 16 y + 452 = 0

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

\frac{y ^{2}}{25} - \frac{( x + 3 ) ^{2}}{56} = 1

\frac{( y + 2 ) ^{2}}{25} - \frac{( x - 3 ) ^{2}}{4} = 1

25 x^{2} - 9 y^{2} = 225

What is the foci ((y-3)^2)/9-((x+1)^2)/(45)=1 ?
The foci ((y-3)^2)/9-((x+1)^2)/(45)=1 is (-1,3+3sqrt(6)),(-1,3-3sqrt(6))