What is the foci ((x-1)^2)/(12^2)-((y-11)^2)/(8^2)=1 ?

The foci ((x-1)^2)/(12^2)-((y-11)^2)/(8^2)=1 is (1+4sqrt(13),11),(1-4sqrt(13),11)

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foci ((x-1)^2)/(12^2)-((y-11)^2)/(8^2)=1

foci

\frac{( x - 1 ) ^{2}}{1 2 ^{2}} - \frac{( y - 11 ) ^{2}}{8 ^{2}} = 1

(1 + 413, 11), (1 - 413, 11)

Solution steps

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

Calculate Hyperbola properties

\frac{( x - 1 ) ^{2}}{1 2 ^{2}} - \frac{( y - 11 ) ^{2}}{8 ^{2}} = 1 :

Right-left Hyperbola with

(h, k) = (1, 11), a = 12, b = 8

(1 + c, 11), (1 - c, 11)

Compute

c :

c = 1 2^{2} + 8^{2} : 413

(1 + 413, 11), (1 - 413, 11)

\frac{( x + 1 ) ^{2}}{4} - \frac{( y - 2 ) ^{2}}{12} = 1

\frac{( y - 3 ) ^{2}}{7} - \frac{( x + 6 ) ^{2}}{42} = 1

\frac{x ^{2}}{3} - \frac{y ^{2}}{3} = 1

2 x^{2} - 3 y^{2} = 6

49 y^{2} - x^{2} = 49

What is the foci ((x-1)^2)/(12^2)-((y-11)^2)/(8^2)=1 ?
The foci ((x-1)^2)/(12^2)-((y-11)^2)/(8^2)=1 is (1+4sqrt(13),11),(1-4sqrt(13),11)