What is the foci x^2-4y^2+8x+16y-4=0 ?

The foci x^2-4y^2+8x+16y-4=0 is (-4+sqrt(5),2),(-4-sqrt(5),2)

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foci x^2-4y^2+8x+16y-4=0

foci

x^{2} - 4 y^{2} + 8 x + 16 y - 4 = 0

(- 4 + 5, 2), (- 4 - 5, 2)

Solution steps

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

Calculate Hyperbola properties

x^{2} - 4 y^{2} + 8 x + 16 y - 4 = 0 :

Right-left Hyperbola with

(h, k) = (- 4, 2), a = 2, b = 1

(- 4 + c, 2), (- 4 - c, 2)

Compute

c :

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

(- 4 + 5, 2), (- 4 - 5, 2)

5 x^{2} - 2 y^{2} + 10 x - 12 y = 23

4 x^{2} - 9 y^{2} - 24 x - 36 y - 36 = 0

9 x^{2} = 4 y^{2} - 12

\frac{( x ^{2} )}{4} - 0.2 y^{2} = 1

\frac{( x + 1 ) ^{2}}{9} - \frac{( y - 4 ) ^{2}}{49} = 1

What is the foci x^2-4y^2+8x+16y-4=0 ?
The foci x^2-4y^2+8x+16y-4=0 is (-4+sqrt(5),2),(-4-sqrt(5),2)