What is the directrix 3y^2-30y+77 ?

The directrix 3y^2-30y+77 is x= 23/12

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directrix 3y^2-30y+77

directrix

3 y^{2} - 30 y + 77

x = \frac{23}{12}

Solution steps

Rewrite

x = 3 y^{2} - 30 y + 77

in the standard form

4 \cdot \frac{1}{12} (x - 2) = (y - 5)^{2}

(h, k) = (2, 5), 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, 5)

x-coordinate

x = 2 - p

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

Refine

x = \frac{23}{12}

(x - 3)^{2} + 1

x^{2} = - 6 y

y = - 12 x^{2} + 4 x

x = \frac{1}{12} y^{2}

x = - 4 (y - 7)^{2} + 7