What is the directrix x=(y-3)^2-4 ?

The directrix x=(y-3)^2-4 is x=-17/4

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directrix x=(y-3)^2-4

directrix

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

x = - \frac{17}{4}

Solution steps

Rewrite

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

in the standard form:

4 \cdot \frac{1}{4} (x - (- 4)) = (y - 3)^{2}

(h, k) = (- 4, 3), p = \frac{1}{4}

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

(- 4, 3)

x-coordinate

x = - 4 - p

x = - 4 - \frac{1}{4}

Refine

x = - \frac{17}{4}

- 30 x^{2} + 28 x - 6

y^{2} - 20 x = 0

x^{2} = 100 y

x = - \frac{1}{4} (y + 6)^{2} + 7

x^{2} + 2 y = 0