What is the foci (x-4)^2=-8(y+4) ?

The foci (x-4)^2=-8(y+4) is (4,-6)

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foci (x-4)^2=-8(y+4)

foci

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

(4, - 6)

Solution steps

Rewrite

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

in the standard form:

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

(h, k) = (4, - 4), p = - 2

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

p

from the center

(4, - 4)

along the y-axis

(4, - 4 + p)

= (4, - 4 + (- 2))

Refine

(4, - 6)

(y - 5)^{2} - 4

- x^{2} = 48 y

3 x^{2} + x - 6

- \frac{1}{20} y^{2}

5 x^{2} - 3 x + 6