What is the foci-4x^2+25y^2-16x-116=0 ?

The foci-4x^2+25y^2-16x-116=0 is (-2,sqrt(29)),(-2,-sqrt(29))

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foci-4x^2+25y^2-16x-116=0

foci

- 4 x^{2} + 25 y^{2} - 16 x - 116 = 0

(- 2, 29), (- 2, - 29)

Solution steps

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

Calculate Hyperbola properties

- 4 x^{2} + 25 y^{2} - 16 x - 116 = 0 :

Up-down Hyperbola with

(h, k) = (- 2, 0), a = 2, b = 5

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

Compute

c :

c = 2^{2} + 5^{2} : 29

(- 2, 0 + 29), (- 2, 0 - 29)

Refine

(- 2, 29), (- 2, - 29)

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

- \frac{( x + 1 ) ^{2}}{25} + \frac{( y + 5 ) ^{2}}{16} = 1

\frac{( x ^{2} )}{4} - 0.12 y^{2} = 1

9 y^{2} - 16 x^{2} = 81

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

What is the foci-4x^2+25y^2-16x-116=0 ?
The foci-4x^2+25y^2-16x-116=0 is (-2,sqrt(29)),(-2,-sqrt(29))