What is the directrix-2x=(y+3)^2+6 ?

The directrix-2x=(y+3)^2+6 is x=-5/2

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directrix-2x=(y+3)^2+6

directrix

- 2 x = (y + 3)^{2} + 6

x = - \frac{5}{2}

Solution steps

Rewrite

- 2 x = (y + 3)^{2} + 6

in the standard form:

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

(h, k) = (- 3, - 3), p = - \frac{1}{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

(- 3, - 3)

x-coordinate

x = - 3 - p

x = - 3 - (- \frac{1}{2})

Refine

x = - \frac{5}{2}

y = \frac{3 x ^{3} - 6 x ^{2}}{x - 2}

- 3 x^{2} + 6 x - 1

(x + 6)^{2} = - 20 (y - 5)

\frac{x ^{3}}{x}

x^{2} + 24 y = 0