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

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

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foci 4x^2-y^2=4

foci

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

(5, 0), (- 5, 0)

Solution steps

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

Calculate Hyperbola properties

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

Right-left Hyperbola with

(h, k) = (0, 0), a = 1, b = 2

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

Compute

c :

c = 1^{2} + 2^{2} : 5

(0 + 5, 0), (0 - 5, 0)

Refine

(5, 0), (- 5, 0)

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

4 x^{2} - y^{2} - 6 y - 25 = 0

\frac{( y - 3 ) ^{2}}{16} - \frac{( x + 4 ) ^{2}}{25} = 1

16 x^{2} - y^{2} - 64 x - 2 y + 47 = 0

\frac{( x - 1 ) ^{2}}{16} - \frac{( y - 7 ) ^{2}}{20} = 1