What is the directrix-1/8 (x-8)^2+2 ?

The directrix-1/8 (x-8)^2+2 is y=4

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directrix-1/8 (x-8)^2+2

directrix

- \frac{1}{8} (x - 8)^{2} + 2

y = 4

Solution steps

Rewrite

y = - \frac{1}{8} (x - 8)^{2} + 2

in the standard form:

4 (- 2) (y - 2) = (x - 8)^{2}

(h, k) = (8, 2), 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

(8, 2)

y-coordinate

y = 2 - p

y = 2 - (- 2)

Refine

y = 4

y = 25 x^{2} - 36

- \frac{1}{2} x^{2} + 7 x - 3

y = - 3 x^{2} + 12 x - 4

y = x^{2} - 2 x + 8

4 y^{2} - 48 x - 20 y = 71