What is the directrix-3(x-1)^2 ?

The directrix-3(x-1)^2 is y= 1/12

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directrix-3(x-1)^2

directrix

- 3 (x - 1)^{2}

y = \frac{1}{12}

Solution steps

Rewrite

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

in the standard form:

4 (- \frac{1}{12}) (y - 0) = (x - 1)^{2}

(h, k) = (1, 0), p = - \frac{1}{12}

Parabola is symmetric around the y-axis and so the directrix is a line parallel to the x-axis, a distance

- p

from the center

(1, 0)

y-coordinate

y = 0 - p

y = 0 - (- \frac{1}{12})

Refine

y = \frac{1}{12}

x = \frac{1}{4} (y + 4)^{2} + 2

2 (x^{2} + 6 x) + 5 y + 8 = 0

10 x^{2}

- 4 x^{2} - 2 x + 1

(x + 5)^{2} = 12 (y - 2)