What is the foci y^2-9x^2=9 ?

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

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foci y^2-9x^2=9

foci

y^{2} - 9 x^{2} = 9

(0, 10), (0, - 10)

Solution steps

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

Calculate Hyperbola properties

y^{2} - 9 x^{2} = 9 :

Up-down Hyperbola with

(h, k) = (0, 0), a = 3, b = 1

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

Compute

c :

c = 3^{2} + 1^{2} : 10

(0, 0 + 10), (0, 0 - 10)

Refine

(0, 10), (0, - 10)

10 y^{2} - 5 x^{2} = 50

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

2 x^{2} - 7 y^{2} - 16 x + 14 y = - 11

9 x^{2} - 4 y^{2} - 36 x + 8 y - 4 = 0

\frac{( x - h ) ^{2}}{64} - \frac{( y - k ) ^{2}}{9} = 1