What is the directrix y-2=3(x-5)^2 ?

The directrix y-2=3(x-5)^2 is y= 23/12

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directrix y-2=3(x-5)^2

directrix

y - 2 = 3 (x - 5)^{2}

y = \frac{23}{12}

Solution steps

Rewrite

y - 2 = 3 (x - 5)^{2}

in the standard form:

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

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

(5, 2)

y-coordinate

y = 2 - p

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

Refine

y = \frac{23}{12}

y = (x - 12)^{2}

x \leq y^{2}

y^{2} = x - 3

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

+ y^{2} - y - x + 1 = 0