What is the foci 9x^2=4y^2-12 ?

The foci 9x^2=4y^2-12 is (0,sqrt(13/3)),(0,-sqrt(13/3))

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foci 9x^2=4y^2-12

foci

9 x^{2} = 4 y^{2} - 12

(0, \frac{13}{3}), (0, - \frac{13}{3})

Solution steps

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

Calculate Hyperbola properties

9 x^{2} = 4 y^{2} - 12 :

Up-down Hyperbola with

(h, k) = (0, 0), a = 3, b = \frac{2}{3}

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

Compute

c :

c = 3^{2} + (\frac{2}{3})^{2} : \frac{13}{3}

(0, 0 + \frac{13}{3}), (0, 0 - \frac{13}{3})

Refine

(0, \frac{13}{3}), (0, - \frac{13}{3})

\frac{( x ^{2} )}{4} - 0.2 y^{2} = 1

\frac{( x + 1 ) ^{2}}{9} - \frac{( y - 4 ) ^{2}}{49} = 1

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

\frac{( y + 2 ) ^{2}}{4} - \frac{( x - 1 ) ^{2}}{16} = 1

x^{2} - 2 x - 3 = y^{2} + 2 y + 3

What is the foci 9x^2=4y^2-12 ?
The foci 9x^2=4y^2-12 is (0,sqrt(13/3)),(0,-sqrt(13/3))