What is the foci ((y-3)^2}{11}-\frac{(x+1)^2)/5 =1 ?

The foci ((y-3)^2}{11}-\frac{(x+1)^2)/5 =1 is (-1,7),(-1,-1)

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foci ((y-3)^2}{11}-\frac{(x+1)^2)/5 =1

foci

\frac{( y - 3 ) ^{2}}{11} - \frac{( x + 1 ) ^{2}}{5} = 1

(- 1, 7), (- 1, - 1)

Solution steps

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

Calculate Hyperbola properties

\frac{( y - 3 ) ^{2}}{11} - \frac{( x + 1 ) ^{2}}{5} = 1 :

Up-down Hyperbola with

(h, k) = (- 1, 3), a = 11, b = 5

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

Compute

c :

c = 11^{2} + 5^{2} : 4

(- 1, 3 + 4), (- 1, 3 - 4)

Refine

(- 1, 7), (- 1, - 1)

x^{2} + 2 x + y^{2} + 4 y = 20

x - y^{2} = 0

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

x^{2} + y^{2} - 2 x - 4 y + 1 = 0

4 x^{2} - y^{2} - 24 x - 4 y + 28 = 0

What is the foci ((y-3)^2}{11}-\frac{(x+1)^2)/5 =1 ?
The foci ((y-3)^2}{11}-\frac{(x+1)^2)/5 =1 is (-1,7),(-1,-1)