What is the directrix x^2=16(y-9) ?

The directrix x^2=16(y-9) is y=5

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directrix x^2=16(y-9)

directrix

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

y = 5

Solution steps

Rewrite

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

in the standard form:

4 \cdot 4 (y - 9) = (x - 0)^{2}

(h, k) = (0, 9), p = 4

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

(0, 9)

y-coordinate

y = 9 - p

y = 9 - 4

Refine

y = 5

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

x = (y + 3)^{2}

13 + 4 x - x^{2}

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

(x - 11)^{2}