What is the foci-x^2+9y^2+90y+189=0 ?

The foci-x^2+9y^2+90y+189=0 is (0,-5+2sqrt(10)),(0,-5-2sqrt(10))

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foci-x^2+9y^2+90y+189=0

foci

- x^{2} + 9 y^{2} + 90 y + 189 = 0

(0, - 5 + 210), (0, - 5 - 210)

Solution steps

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

Calculate Hyperbola properties

- x^{2} + 9 y^{2} + 90 y + 189 = 0 :

Up-down Hyperbola with

(h, k) = (0, - 5), a = 2, b = 6

(0, - 5 + c), (0, - 5 - c)

Compute

c :

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

(0, - 5 + 210), (0, - 5 - 210)

\frac{( y - 3 ) ^{2}}{9} - \frac{( x + 1 ) ^{2}}{45} = 1

36 x^{2} - 4 y^{2} - 216 x + 16 y + 452 = 0

2 y^{2} - \frac{x ^{2}}{2} = 2

\frac{y ^{2}}{25} - \frac{( x + 3 ) ^{2}}{56} = 1

\frac{( y + 2 ) ^{2}}{25} - \frac{( x - 3 ) ^{2}}{4} = 1

What is the foci-x^2+9y^2+90y+189=0 ?
The foci-x^2+9y^2+90y+189=0 is (0,-5+2sqrt(10)),(0,-5-2sqrt(10))