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

The foci x=x^2-(y^2)/9 is ((1+sqrt(10))/2 ,0),((1-sqrt(10))/2 ,0)

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foci x=x^2-(y^2)/9

foci

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

(\frac{1 + 10}{2}, 0), (\frac{1 - 10}{2}, 0)

Solution steps

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

Calculate Hyperbola properties

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

Right-left Hyperbola with

(h, k) = (\frac{1}{2}, 0), a = \frac{1}{2}, b = \frac{3}{2}

(\frac{1}{2} + c, 0), (\frac{1}{2} - c, 0)

Compute

c :

c = (\frac{1}{2})^{2} + (\frac{3}{2})^{2} : \frac{5}{2}

(\frac{1}{2} + \frac{5}{2}, 0), (\frac{1}{2} - \frac{5}{2}, 0)

Refine

(\frac{1 + 10}{2}, 0), (\frac{1 - 10}{2}, 0)

11 x^{2} - 7 y^{2} = 77

9 x^{2} - 4 y^{2} = 144

\frac{( x - 5 ) ^{2}}{16} - \frac{( y - 4 ) ^{2}}{64} = 1

8 x^{2} - 2 y^{2} = 16

4 x^{2} - 12 y^{2} - 16 x - 72 y - 44 = 0

What is the foci x=x^2-(y^2)/9 ?
The foci x=x^2-(y^2)/9 is ((1+sqrt(10))/2 ,0),((1-sqrt(10))/2 ,0)