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

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

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

foci

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

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

Solution steps

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

Calculate Hyperbola properties

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

Right-left Hyperbola with

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

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

Compute

c :

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

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

\frac{x ^{2}}{81} - \frac{y ^{2}}{9} = 1

\frac{y ^{2}}{16} - \frac{x ^{2}}{49} = 1

\frac{y ^{2}}{25} - \frac{x ^{2}}{144} = 1

9 y^{2} - x^{2} + 2 x + 54 y + 62 = 0

16 x^{2} - 25 y^{2} = 400

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