What is the foci-9x^2+4y^2-36x-16y-164=0 ?

The foci-9x^2+4y^2-36x-16y-164=0 is (-2,2+2sqrt(13)),(-2,2-2sqrt(13))

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foci-9x^2+4y^2-36x-16y-164=0

foci

- 9 x^{2} + 4 y^{2} - 36 x - 16 y - 164 = 0

(- 2, 2 + 213), (- 2, 2 - 213)

Solution steps

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

Calculate Hyperbola properties

- 9 x^{2} + 4 y^{2} - 36 x - 16 y - 164 = 0 :

Up-down Hyperbola with

(h, k) = (- 2, 2), a = 6, b = 4

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

Compute

c :

c = 6^{2} + 4^{2} : 213

(- 2, 2 + 213), (- 2, 2 - 213)

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

- \frac{( x - 2 ) ^{2}}{9} + \frac{( y + 1 ) ^{2}}{5} = 1

- 25 x^{2} + 4 y^{2} + 150 x + 24 y - 289 = 0

9 x^{2} - 16 y^{2} + 36 x + 32 y - 124 = 0

- \frac{x ^{2}}{a ^{2}} + \frac{y ^{2}}{b ^{2}} = 1

What is the foci-9x^2+4y^2-36x-16y-164=0 ?
The foci-9x^2+4y^2-36x-16y-164=0 is (-2,2+2sqrt(13)),(-2,2-2sqrt(13))