What is the foci 9x^2-36x-4y^2-24y-36=0 ?

The foci 9x^2-36x-4y^2-24y-36=0 is (2+sqrt(13),-3),(2-sqrt(13),-3)

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foci 9x^2-36x-4y^2-24y-36=0

foci

9 x^{2} - 36 x - 4 y^{2} - 24 y - 36 = 0

(2 + 13, - 3), (2 - 13, - 3)

Solution steps

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

Calculate Hyperbola properties

9 x^{2} - 36 x - 4 y^{2} - 24 y - 36 = 0 :

Right-left Hyperbola with

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

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

Compute

c :

c = 2^{2} + 3^{2} : 13

(2 + 13, - 3), (2 - 13, - 3)

\frac{( x - 3 ) ^{2}}{81} - \frac{( y + 5 ) ^{2}}{144} = 1

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

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

\frac{x ^{2}}{140} - \frac{( y - 6 ) ^{2}}{4} = - 1

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

What is the foci 9x^2-36x-4y^2-24y-36=0 ?
The foci 9x^2-36x-4y^2-24y-36=0 is (2+sqrt(13),-3),(2-sqrt(13),-3)