What is the foci y^2-4y-4x^2+13=0 ?

The foci y^2-4y-4x^2+13=0 is ((3sqrt(5))/2 ,2),(-(3sqrt(5))/2 ,2)

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foci y^2-4y-4x^2+13=0

foci

y^{2} - 4 y - 4 x^{2} + 13 = 0

(\frac{3 5}{2}, 2), (- \frac{3 5}{2}, 2)

Solution steps

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

Calculate Hyperbola properties

y^{2} - 4 y - 4 x^{2} + 13 = 0 :

Right-left Hyperbola with

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

(0 + c, 2), (0 - c, 2)

Compute

c :

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

(0 + \frac{3 5}{2}, 2), (0 - \frac{3 5}{2}, 2)

Refine

(\frac{3 5}{2}, 2), (- \frac{3 5}{2}, 2)

\frac{( x - 3 ) ^{2}}{9} - \frac{( y + 10 ) ^{2}}{100} = 1

4 x^{2} - 12 y^{2} - 24 x + 24 y + 51 = 0

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

x^{2} - 9 y^{2} - 4 x + 36 y - 41 = 0

4 y^{2} - 9 x^{2} + 40 y - 540 x - 8036 = 0

What is the foci y^2-4y-4x^2+13=0 ?
The foci y^2-4y-4x^2+13=0 is ((3sqrt(5))/2 ,2),(-(3sqrt(5))/2 ,2)