What is the foci+9x^2-y^2-36x-6y+18=0 ?

The foci+9x^2-y^2-36x-6y+18=0 is (2+sqrt(10),-3),(2-sqrt(10),-3)

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foci+9x^2-y^2-36x-6y+18=0

foci

+ 9 x^{2} - y^{2} - 36 x - 6 y + 18 = 0

(2 + 10, - 3), (2 - 10, - 3)

Solution steps

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

Calculate Hyperbola properties

+ 9 x^{2} - y^{2} - 36 x - 6 y + 18 = 0 :

Right-left Hyperbola with

(h, k) = (2, - 3), a = 1, b = 3

(2 + c, - 3), (2 - c, - 3)

Compute

c :

c = 1^{2} + 3^{2} : 10

(2 + 10, - 3), (2 - 10, - 3)

\frac{( y + 5 ) ^{2}}{16} - \frac{( x + 3 ) ^{2}}{9} = 1

\frac{( y + 5 ) ^{2}}{\frac{1}{9}} - \frac{( x - 3 ) ^{2}}{\frac{1}{4}} = 1

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

\frac{( x + 3 ) ^{2}}{25} - \frac{( y - 2 ) ^{2}}{49} = 1

4 y^{2} - x^{2} = 900

What is the foci+9x^2-y^2-36x-6y+18=0 ?
The foci+9x^2-y^2-36x-6y+18=0 is (2+sqrt(10),-3),(2-sqrt(10),-3)