What is the foci-9x^2+y^2+6y-27=0 ?

The foci-9x^2+y^2+6y-27=0 is (0,-3+2sqrt(10)),(0,-3-2sqrt(10))

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foci-9x^2+y^2+6y-27=0

foci

- 9 x^{2} + y^{2} + 6 y - 27 = 0

(0, - 3 + 210), (0, - 3 - 210)

Solution steps

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

Calculate Hyperbola properties

- 9 x^{2} + y^{2} + 6 y - 27 = 0 :

Up-down Hyperbola with

(h, k) = (0, - 3), a = 6, b = 2

(0, - 3 + c), (0, - 3 - c)

Compute

c :

c = 6^{2} + 2^{2} : 210

(0, - 3 + 210), (0, - 3 - 210)

x^{2} - 4 y^{2} - 8 = 0

\frac{( y + 1 ) ^{2}}{49} - \frac{( x + 3 ) ^{2}}{64} = 1

289 y^{2} - x^{2} = 1

\frac{( x + 2 ) ^{2}}{16} - \frac{( y - 3 ) ^{2}}{9} = 1

\frac{( x + 2 ) ^{2}}{49} - \frac{( y - 2 ) ^{2}}{45} = 1

What is the foci-9x^2+y^2+6y-27=0 ?
The foci-9x^2+y^2+6y-27=0 is (0,-3+2sqrt(10)),(0,-3-2sqrt(10))