What is the foci (x+3)^2=24(y-1) ?

The foci (x+3)^2=24(y-1) is (-3,7)

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foci (x+3)^2=24(y-1)

foci

(x + 3)^{2} = 24 (y - 1)

(- 3, 7)

Solution steps

Rewrite

(x + 3)^{2} = 24 (y - 1)

in the standard form:

4 \cdot 6 (y - 1) = (x - (- 3))^{2}

(h, k) = (- 3, 1), p = 6

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

p

from the center

(- 3, 1)

along the y-axis

(- 3, 1 + p)

= (- 3, 1 + 6)

Refine

(- 3, 7)

3 - 2 x - x^{2}

x^{2} + x - 1

y = - x^{2} + 2

(y - 5)^{2} = 12 (x + 3)

y = 2 x^{2} + 16 x + 29