What is the foci 9x^2-4y^2-90x-32y=-305 ?

The foci 9x^2-4y^2-90x-32y=-305 is (5,-4+2sqrt(13)),(5,-4-2sqrt(13))

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foci 9x^2-4y^2-90x-32y=-305

foci

9 x^{2} - 4 y^{2} - 90 x - 32 y = - 305

(5, - 4 + 213), (5, - 4 - 213)

Solution steps

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

Calculate Hyperbola properties

9 x^{2} - 4 y^{2} - 90 x - 32 y = - 305 :

Up-down Hyperbola with

(h, k) = (5, - 4), a = 6, b = 4

(5, - 4 + c), (5, - 4 - c)

Compute

c :

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

(5, - 4 + 213), (5, - 4 - 213)

\frac{( y - 2 ) ^{2}}{40} - \frac{( x - 4 ) ^{2}}{9} = 1

5 y^{2} - 16 x^{2} + 400 = 0

\frac{x ^{2}}{36} - \frac{( y - 10 ) ^{2}}{64} = 1

\frac{( y - 1 ) ^{2}}{49} - \frac{( x - 2 ) ^{2}}{32} = 1

\frac{( x - 3 ) ^{2}}{13} - \frac{( y - 5 ) ^{2}}{7} = 1

What is the foci 9x^2-4y^2-90x-32y=-305 ?
The foci 9x^2-4y^2-90x-32y=-305 is (5,-4+2sqrt(13)),(5,-4-2sqrt(13))