What is the foci y^2-9x^2-8y-54x-81=0 ?

The foci y^2-9x^2-8y-54x-81=0 is (-3,(12+4sqrt(10))/3),(-3,(12-4sqrt(10))/3)

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foci y^2-9x^2-8y-54x-81=0

foci

y^{2} - 9 x^{2} - 8 y - 54 x - 81 = 0

(- 3, \frac{12 + 4 10}{3}), (- 3, \frac{12 - 4 10}{3})

Solution steps

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

Calculate Hyperbola properties

y^{2} - 9 x^{2} - 8 y - 54 x - 81 = 0 :

Up-down Hyperbola with

(h, k) = (- 3, 4), a = 4, b = \frac{4}{3}

(- 3, 4 + c), (- 3, 4 - c)

Compute

c :

c = 4^{2} + (\frac{4}{3})^{2} : \frac{4 10}{3}

(- 3, 4 + \frac{4 10}{3}), (- 3, 4 - \frac{4 10}{3})

Refine

(- 3, \frac{12 + 4 10}{3}), (- 3, \frac{12 - 4 10}{3})

\frac{( x - 3 ) ^{2}}{8 ^{2}} - \frac{( y - 2 ) ^{2}}{8 ^{2}} = 1

\frac{x ^{2}}{49} - \frac{y ^{2}}{81} = 1

\frac{y ^{2}}{6} - \frac{x ^{2}}{11} = 1

4 x^{2} - y^{2} - 32 x + 60 = 0

\frac{x ^{2}}{625} - \frac{y ^{2}}{3600} = 1

What is the foci y^2-9x^2-8y-54x-81=0 ?
The foci y^2-9x^2-8y-54x-81=0 is (-3,(12+4sqrt(10))/3),(-3,(12-4sqrt(10))/3)