What is the foci 289y^2-x^2=1 ?

The foci 289y^2-x^2=1 is (0,(sqrt(290))/(17)),(0,-(sqrt(290))/(17))

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foci 289y^2-x^2=1

foci

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

(0, \frac{290}{17}), (0, - \frac{290}{17})

Solution steps

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

Calculate Hyperbola properties

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

Up-down Hyperbola with

(h, k) = (0, 0), a = \frac{1}{17}, b = 1

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

Compute

c :

c = (\frac{1}{17})^{2} + 1^{2} : \frac{290}{17}

(0, 0 + \frac{290}{17}), (0, 0 - \frac{290}{17})

Refine

(0, \frac{290}{17}), (0, - \frac{290}{17})

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

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

\frac{( y - 3 ) ^{2}}{8 ^{2}} - \frac{( x - 2 ) ^{2}}{8 ^{2}} = 1

\frac{x ^{2}}{18} - \frac{y ^{2}}{7} = 1

\frac{( x ^{2} )}{4} - 0.14 y^{2} = 1

What is the foci 289y^2-x^2=1 ?
The foci 289y^2-x^2=1 is (0,(sqrt(290))/(17)),(0,-(sqrt(290))/(17))