What is the foci 16y^2-x^2+2x+64y+47=0 ?

The foci 16y^2-x^2+2x+64y+47=0 is (1,-2+sqrt(17)),(1,-2-sqrt(17))

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foci 16y^2-x^2+2x+64y+47=0

foci

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

(1, - 2 + 17), (1, - 2 - 17)

Solution steps

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

Calculate Hyperbola properties

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

Up-down Hyperbola with

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

(1, - 2 + c), (1, - 2 - c)

Compute

c :

c = 1^{2} + 4^{2} : 17

(1, - 2 + 17), (1, - 2 - 17)

\frac{( x + 1 ) ^{2}}{9} - \frac{( y - 3 ) ^{2}}{16} = 1

\frac{x ^{2}}{25} - \frac{y ^{2}}{64} = 1

\frac{x ^{2}}{4} - \frac{y ^{2}}{12} = 1

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

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

What is the foci 16y^2-x^2+2x+64y+47=0 ?
The foci 16y^2-x^2+2x+64y+47=0 is (1,-2+sqrt(17)),(1,-2-sqrt(17))