What is the foci y^2-12y-4x=-28 ?

The foci y^2-12y-4x=-28 is (-1,6)

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foci y^2-12y-4x=-28

foci

y^{2} - 12 y - 4 x = - 28

(- 1, 6)

Solution steps

Rewrite

y^{2} - 12 y - 4 x = - 28

in the standard form

4 \cdot 1 \cdot (x - (- 2)) = (y - 6)^{2}

(h, k) = (- 2, 6), p = 1

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

p

from the center

(- 2, 6)

along the x-axis

(- 2 + p, 6)

= (- 2 + 1, 6)

Refine

(- 1, 6)

(x - 1)^{2} = 8 (y - k)

(y - 4)^{2} = 8 (x - 3)

y = 16 x^{2} - 25

+ 2 x^{2} - 3 x - 1

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