What is the directrix x^2-2x-4y+9=0 ?

The directrix x^2-2x-4y+9=0 is y=1

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directrix x^2-2x-4y+9=0

directrix

x^{2} - 2 x - 4 y + 9 = 0

y = 1

Solution steps

Rewrite

x^{2} - 2 x - 4 y + 9 = 0

in the standard form

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

(h, k) = (1, 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

(1, 2)

y-coordinate

y = 2 - p

y = 2 - 1

Refine

y = 1

\frac{- 3 x ^{2} - 2 x + 6}{5}

3 x^{2} - x - 2

y = - 3 x^{2} - 12 x - 9

y = \frac{1}{8} x^{2}

- 2 x^{2} + 5 x - 6