What is the directrix 2(y-1)^2-4 ?

The directrix 2(y-1)^2-4 is x=-33/8

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directrix 2(y-1)^2-4

directrix

2 (y - 1)^{2} - 4

x = - \frac{33}{8}

Solution steps

Rewrite

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

in the standard form:

4 \cdot \frac{1}{8} (x - (- 4)) = (y - 1)^{2}

(h, k) = (- 4, 1), p = \frac{1}{8}

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

(- 4, 1)

x-coordinate

x = - 4 - p

x = - 4 - \frac{1}{8}

Refine

x = - \frac{33}{8}

x = - \frac{1}{2} (y - 2)^{2} + 5

y = 48 x - 8 x^{2}

x^{2} + 4 x + 4 y = - 4

y = - 2 x^{2}

y = 2 x^{2} - 3