What is the directrix x=2y^2 ?

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directrix x=2y^2

directrix

x = 2 y^{2}

x = - \frac{1}{8}

Solution steps

Rewrite

x = 2 y^{2}

in the standard form:

4 \cdot \frac{1}{8} (x - 0) = (y - 0)^{2}

(h, k) = (0, 0), 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

(0, 0)

x-coordinate

x = 0 - p

x = 0 - \frac{1}{8}

Refine

x = - \frac{1}{8}

0 = - \frac{400}{9} x^{2} + 16 y^{2} + 400

5 x^{2} + 7 y = 3

41 x^{2} + 16 y^{2} + 246 x - 192 y + 289 = 0

x^{2} + 14 x + y^{2} - 6 y - 23 = 0

x = 2 y - y^{2}