What is the foci ((x-6)^2)/4-((y+6)^2)/(81)=1 ?

The foci ((x-6)^2)/4-((y+6)^2)/(81)=1 is (6+sqrt(85),-6),(6-sqrt(85),-6)

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foci ((x-6)^2)/4-((y+6)^2)/(81)=1

foci

\frac{( x - 6 ) ^{2}}{4} - \frac{( y + 6 ) ^{2}}{81} = 1

(6 + 85, - 6), (6 - 85, - 6)

Solution steps

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

Calculate Hyperbola properties

\frac{( x - 6 ) ^{2}}{4} - \frac{( y + 6 ) ^{2}}{81} = 1 :

Right-left Hyperbola with

(h, k) = (6, - 6), a = 2, b = 9

(6 + c, - 6), (6 - c, - 6)

Compute

c :

c = 2^{2} + 9^{2} : 85

(6 + 85, - 6), (6 - 85, - 6)

\frac{( x + 2 ) ^{2}}{9} - \frac{( y - 1 ) ^{2}}{4} = 1

x^{2} - y^{2} = 13

\frac{( y ) ^{2}}{81} - \frac{( x ) ^{2}}{121} = 1

x^{2} - y^{2} = 15

x^{2} - 10 x = 4 y^{2} - 5

What is the foci ((x-6)^2)/4-((y+6)^2)/(81)=1 ?
The foci ((x-6)^2)/4-((y+6)^2)/(81)=1 is (6+sqrt(85),-6),(6-sqrt(85),-6)