What is the foci y^2-9x^2-36x-8y-29=0 ?

The foci y^2-9x^2-36x-8y-29=0 is (-2,4+sqrt(10)),(-2,4-sqrt(10))

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foci y^2-9x^2-36x-8y-29=0

foci

y^{2} - 9 x^{2} - 36 x - 8 y - 29 = 0

(- 2, 4 + 10), (- 2, 4 - 10)

Solution steps

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

Calculate Hyperbola properties

y^{2} - 9 x^{2} - 36 x - 8 y - 29 = 0 :

Up-down Hyperbola with

(h, k) = (- 2, 4), a = 3, b = 1

(- 2, 4 + c), (- 2, 4 - c)

Compute

c :

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

(- 2, 4 + 10), (- 2, 4 - 10)

x^{2} - y^{2} - 4 x - 2 y - 13 = 0

\frac{( x - 3 ) ^{2}}{9} - \frac{( y - 2 ) ^{2}}{22} = 1

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

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

\frac{( y + \frac{9}{2} ) ^{2}}{25} - \frac{( x - \frac{7}{2} ) ^{2}}{25} = 1

What is the foci y^2-9x^2-36x-8y-29=0 ?
The foci y^2-9x^2-36x-8y-29=0 is (-2,4+sqrt(10)),(-2,4-sqrt(10))