What is the foci 9x^2-4y^2+36x+8y+33=0 ?

The foci 9x^2-4y^2+36x+8y+33=0 is (-2,(6+sqrt(13))/6),(-2,(6-sqrt(13))/6)

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foci 9x^2-4y^2+36x+8y+33=0

foci

9 x^{2} - 4 y^{2} + 36 x + 8 y + 33 = 0

(- 2, \frac{6 + 13}{6}), (- 2, \frac{6 - 13}{6})

Solution steps

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

Calculate Hyperbola properties

9 x^{2} - 4 y^{2} + 36 x + 8 y + 33 = 0 :

Up-down Hyperbola with

(h, k) = (- 2, 1), a = \frac{1}{2}, b = \frac{1}{3}

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

Compute

c :

c = (\frac{1}{2})^{2} + (\frac{1}{3})^{2} : \frac{13}{6}

(- 2, 1 + \frac{13}{6}), (- 2, 1 - \frac{13}{6})

Refine

(- 2, \frac{6 + 13}{6}), (- 2, \frac{6 - 13}{6})

\frac{y ^{2}}{4} - \frac{x ^{2}}{25} = 1

25 y^{2} - 36 (x - 8)^{2} = 900

\frac{y ^{2}}{16} - \frac{x ^{2}}{36} = 1

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

9 x^{2} - y^{2} = 36

What is the foci 9x^2-4y^2+36x+8y+33=0 ?
The foci 9x^2-4y^2+36x+8y+33=0 is (-2,(6+sqrt(13))/6),(-2,(6-sqrt(13))/6)