What is the foci ((y+2)^2)/(25)-((x-9)^2)/(81)=1 ?

The foci ((y+2)^2)/(25)-((x-9)^2)/(81)=1 is (9,-2+sqrt(106)),(9,-2-sqrt(106))

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foci ((y+2)^2)/(25)-((x-9)^2)/(81)=1

foci

\frac{( y + 2 ) ^{2}}{25} - \frac{( x - 9 ) ^{2}}{81} = 1

(9, - 2 + 106), (9, - 2 - 106)

Solution steps

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

Calculate Hyperbola properties

\frac{( y + 2 ) ^{2}}{25} - \frac{( x - 9 ) ^{2}}{81} = 1 :

Up-down Hyperbola with

(h, k) = (9, - 2), a = 5, b = 9

(9, - 2 + c), (9, - 2 - c)

Compute

c :

c = 5^{2} + 9^{2} : 106

(9, - 2 + 106), (9, - 2 - 106)

4 x^{2} - 9 y^{2} + 32 x - 18 y + 37 = 0

- 4 x^{2} + y^{2} + 40 x - 136 = 0

\frac{y ^{2}}{225} - \frac{x ^{2}}{324} = 1

- x^{2} + 8 x + 4 y^{2} - 40 y + 88 = 0

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

What is the foci ((y+2)^2)/(25)-((x-9)^2)/(81)=1 ?
The foci ((y+2)^2)/(25)-((x-9)^2)/(81)=1 is (9,-2+sqrt(106)),(9,-2-sqrt(106))