What is the foci ((y-2)^2)/4-((x-1)^2)/1 =1 ?

The foci ((y-2)^2)/4-((x-1)^2)/1 =1 is (1,2+sqrt(5)),(1,2-sqrt(5))

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foci ((y-2)^2)/4-((x-1)^2)/1 =1

foci

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

(1, 2 + 5), (1, 2 - 5)

Solution steps

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

Calculate Hyperbola properties

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

Up-down Hyperbola with

(h, k) = (1, 2), a = 2, b = 1

(1, 2 + c), (1, 2 - c)

Compute

c :

c = 2^{2} + 1^{2} : 5

(1, 2 + 5), (1, 2 - 5)

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

y^{2} - 4 x^{2} = 36

\frac{( y - 2 ) ^{2}}{14} - \frac{( x + 6 ) ^{2}}{3} = 4

3 x^{2} - 13 y^{2} - 30 x + 52 y = 16

4 x^{2} + 9 y^{2} + 3 x - 18 y^{2} + 37 = 0

What is the foci ((y-2)^2)/4-((x-1)^2)/1 =1 ?
The foci ((y-2)^2)/4-((x-1)^2)/1 =1 is (1,2+sqrt(5)),(1,2-sqrt(5))