What is the directrix x=3y^2-6y+5 ?

The directrix x=3y^2-6y+5 is x= 23/12

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directrix x=3y^2-6y+5

directrix

x = 3 y^{2} - 6 y + 5

x = \frac{23}{12}

Solution steps

Rewrite

x = 3 y^{2} - 6 y + 5

in the standard form

4 \cdot \frac{1}{12} (x - 2) = (y - 1)^{2}

(h, k) = (2, 1), p = \frac{1}{12}

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

(2, 1)

x-coordinate

x = 2 - p

x = 2 - \frac{1}{12}

Refine

x = \frac{23}{12}

(y + 1)^{2} = 12 x

(y - 2)^{2} = 40 (x - 2)

(x - 3)^{2} - 1

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

y = - 3 x^{2} + 5 x