What is the directrix 2y^2=-5x ?

The directrix 2y^2=-5x is x= 5/8

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directrix 2y^2=-5x

directrix

2 y^{2} = - 5 x

x = \frac{5}{8}

Solution steps

Rewrite

2 y^{2} = - 5 x

in the standard form:

4 (- \frac{5}{8}) (x - 0) = (y - 0)^{2}

(h, k) = (0, 0), p = - \frac{5}{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{5}{8})

Refine

x = \frac{5}{8}

12 (x - 1) = (y - 3)^{2}

y = \frac{1}{4} x^{2} - \frac{5}{2} x + \frac{13}{4}

4 x^{2} - 25

y = - 6 x^{2} + 37 x + 13

x^{2} = - 24 y