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}

x^{2} = 16 (y - 9)

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

x = (y + 3)^{2}

13 + 4 x - x^{2}

y = s^{2} + 2 s + 2