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

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

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

directrix

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

x = \frac{23}{12}

Solution steps

Rewrite

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

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^{2} - 2 x - 24

18 x^{2} - 64 x - 14 y + 150 = 0

2 x^{2} + 5 x

y = - \frac{1}{14} x^{2} + 2

2 y^{2} = 16 x