What is the directrix 2y^2+x+20y+51=0 ?

The directrix 2y^2+x+20y+51=0 is x=-7/8

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directrix 2y^2+x+20y+51=0

directrix

2 y^{2} + x + 20 y + 51 = 0

x = - \frac{7}{8}

Solution steps

Rewrite

2 y^{2} + x + 20 y + 51 = 0

in the standard form

4 (- \frac{1}{8}) (x - (- 1)) = (y - (- 5))^{2}

(h, k) = (- 1, - 5), 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

(- 1, - 5)

x-coordinate

x = - 1 - p

x = - 1 - (- \frac{1}{8})

Refine

x = - \frac{7}{8}

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

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

y^{2} - 8 y + 4 x = 0

x^{2} + 4 x + 6 y - 2 = 0

48 x - 6 x^{2}