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

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

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foci ((x-5)^2)/1-((y-4)^2)/1 =1

foci

\frac{( x - 5 ) ^{2}}{1} - \frac{( y - 4 ) ^{2}}{1} = 1

(5 + 2, 4), (5 - 2, 4)

Solution steps

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

Calculate Hyperbola properties

\frac{( x - 5 ) ^{2}}{1} - \frac{( y - 4 ) ^{2}}{1} = 1 :

Right-left Hyperbola with

(h, k) = (5, 4), a = 1, b = 1

(5 + c, 4), (5 - c, 4)

Compute

c :

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

(5 + 2, 4), (5 - 2, 4)

9 x^{2} - 4 y^{2} - 54 x - 8 y + 113 = 0

\frac{( y - 2 ) ^{2}}{9} - \frac{( x - 1 ) ^{2}}{16} = 1

x^{2} - 3 y^{2} + 12 = 0

9 x^{2} - 9 y^{2} - 18 x + 54 = 0

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

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