What is the directrix ((x-3)^2)/8+5 ?

The directrix ((x-3)^2)/8+5 is y=3

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directrix ((x-3)^2)/8+5

directrix

\frac{( x - 3 ) ^{2}}{8} + 5

y = 3

Solution steps

Rewrite

y = \frac{( x - 3 ) ^{2}}{8} + 5

in the standard form:

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

(h, k) = (3, 5), p = 2

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

(3, 5)

y-coordinate

y = 5 - p

y = 5 - 2

Refine

y = 3

x = 3 y^{2} - 6 y + 5

(y + 1)^{2} = 12 x

(y - 2)^{2} = 40 (x - 2)

(x - 3)^{2} - 1

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