What is the foci 4x^2-y^2+12x+5=0 ?

The foci 4x^2-y^2+12x+5=0 is ((-3+2sqrt(5))/2 ,0),((-3-2sqrt(5))/2 ,0)

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foci 4x^2-y^2+12x+5=0

foci

4 x^{2} - y^{2} + 12 x + 5 = 0

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

Solution steps

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

Calculate Hyperbola properties

4 x^{2} - y^{2} + 12 x + 5 = 0 :

Right-left Hyperbola with

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

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

Compute

c :

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

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

Refine

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

\frac{( x - 13 ) ^{2}}{144} - \frac{y ^{2}}{25} = 1

9 x^{2} - 4 y^{2} - 90 x - 32 y = - 305

\frac{( y - 2 ) ^{2}}{40} - \frac{( x - 4 ) ^{2}}{9} = 1

5 y^{2} - 16 x^{2} + 400 = 0

\frac{x ^{2}}{36} - \frac{( y - 10 ) ^{2}}{64} = 1

What is the foci 4x^2-y^2+12x+5=0 ?
The foci 4x^2-y^2+12x+5=0 is ((-3+2sqrt(5))/2 ,0),((-3-2sqrt(5))/2 ,0)