What is the directrix x^2-4x-y+3=0 ?

The directrix x^2-4x-y+3=0 is y=-5/4

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directrix x^2-4x-y+3=0

directrix

x^{2} - 4 x - y + 3 = 0

y = - \frac{5}{4}

Solution steps

Rewrite

x^{2} - 4 x - y + 3 = 0

in the standard form

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

(h, k) = (2, - 1), p = \frac{1}{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

(2, - 1)

y-coordinate

y = - 1 - p

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

Refine

y = - \frac{5}{4}

y = - 3 (x - 2) (x + 5)

5 x^{2} + 4 x - 9

y^{2} + 4 y + 3

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

y = - 6 (x - 8)^{2} - 4