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

The directrix y^2+33=-8x-23 is x=-5

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

directrix

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

x = - 5

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 directrix is a line parallel to the y-axis, a distance

- p

from the center

(- 7, 0)

x-coordinate

x = - 7 - p

x = - 7 - (- 2)

Refine

x = - 5

x^{2} + 7 x + 12

- x^{2} + 1

- x^{2} + 7

y = - 16 x^{2} + 16 x + 480

- x^{2} + 5 x - 7