What is the foci y^2+33=-8x-23 ?

The foci y^2+33=-8x-23 is (-9,0)

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foci y^2+33=-8x-23

foci

y^{2} + 33 = - 8 x - 23

(- 9, 0)

Solution steps

Rewrite

y^{2} + 33 = - 8 x - 23

in the standard form:

4 (- 2) (x - (- 7)) = (y - 0)^{2}

(h, k) = (- 7, 0), p = - 2

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

p

from the center

(- 7, 0)

along the x-axis

(- 7 + p, 0)

= (- 7 + (- 2), 0)

Refine

(- 9, 0)

x^{2} - x + 3

4 x^{2} + 8

y^{2} + 8 x + 2 y + 33 = 0

(2 x + 5)^{2}

x = (2 y + 5)^{2}