What is the foci 4y^2-x^2+6x+8y+4=0 ?

The foci 4y^2-x^2+6x+8y+4=0 is ((6+3sqrt(5))/2 ,-1),((6-3sqrt(5))/2 ,-1)

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foci 4y^2-x^2+6x+8y+4=0

foci

(\frac{6 + 3 5}{2}, - 1), (\frac{6 - 3 5}{2}, - 1)

Solution steps

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

Calculate Hyperbola properties

4 y^{2} - x^{2} + 6 x + 8 y + 4 = 0 :

Right-left Hyperbola with

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

(3 + c, - 1), (3 - c, - 1)

Compute

c :

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

(3 + \frac{3 5}{2}, - 1), (3 - \frac{3 5}{2}, - 1)

Refine

(\frac{6 + 3 5}{2}, - 1), (\frac{6 - 3 5}{2}, - 1)

What is the foci 4y^2-x^2+6x+8y+4=0 ?
The foci 4y^2-x^2+6x+8y+4=0 is ((6+3sqrt(5))/2 ,-1),((6-3sqrt(5))/2 ,-1)