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

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

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

foci

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

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

Solution steps

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

Calculate Hyperbola properties

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

Right-left Hyperbola with

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

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

Compute

c :

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

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

9 x^{2} = 4 y^{2} - 12

\frac{( x ^{2} )}{4} - 0.2 y^{2} = 1

\frac{( x + 1 ) ^{2}}{9} - \frac{( y - 4 ) ^{2}}{49} = 1

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

\frac{( y + 2 ) ^{2}}{4} - \frac{( x - 1 ) ^{2}}{16} = 1

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