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

The foci y^2-4y+4x=-16 is (-4,2)

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

foci

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

(- 4, 2)

Solution steps

Rewrite

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

in the standard form

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

(h, k) = (- 3, 2), p = - 1

Parabola is symmetric around the x-axis and so the focus lies a distance

p

from the center

(- 3, 2)

along the x-axis

(- 3 + p, 2)

= (- 3 + (- 1), 2)

Refine

(- 4, 2)

\frac{x ^{2}}{16} - \frac{y ^{2}}{36} = 1

x^{2} + y^{2} - 2 x + 6 y + 9 = 0

\frac{( x + 3 ) ^{2}}{16} + \frac{( y - 5 ) ^{2}}{25} = 1

\frac{x ^{2}}{9} + \frac{y ^{2}}{5} = 1

y^{2} = 5 x