What is the directrix x^2=4(y-2) ?

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

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directrix x^2=4(y-2)

directrix

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

y = 1

Solution steps

Rewrite

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

in the standard form:

4 \cdot 1 \cdot (y - 2) = (x - 0)^{2}

(h, k) = (0, 2), p = 1

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, 2)

y-coordinate

y = 2 - p

y = 2 - 1

Refine

y = 1

x = + \frac{17}{4} (y + 2)^{2}

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

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

y = x^{2} - 4 x + 9

(3 x - 2) (2 x + 1)