What is the foci 9x^2-4y^2-36x+8y-4=0 ?

The foci 9x^2-4y^2-36x+8y-4=0 is (2+sqrt(13),1),(2-sqrt(13),1)

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foci 9x^2-4y^2-36x+8y-4=0

foci

9 x^{2} - 4 y^{2} - 36 x + 8 y - 4 = 0

(2 + 13, 1), (2 - 13, 1)

Solution steps

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

Calculate Hyperbola properties

9 x^{2} - 4 y^{2} - 36 x + 8 y - 4 = 0 :

Right-left Hyperbola with

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

(2 + c, 1), (2 - c, 1)

Compute

c :

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

(2 + 13, 1), (2 - 13, 1)

\frac{( x - h ) ^{2}}{64} - \frac{( y - k ) ^{2}}{9} = 1

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

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

12 y^{2} - 4 x^{2} + 16 x + 72 y + 44 = 0

\frac{y ^{2}}{45} - \frac{x ^{2}}{36} = 1

What is the foci 9x^2-4y^2-36x+8y-4=0 ?
The foci 9x^2-4y^2-36x+8y-4=0 is (2+sqrt(13),1),(2-sqrt(13),1)