What is the directrix x^2-2x-4y+13=0 ?

The directrix x^2-2x-4y+13=0 is y=2

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directrix x^2-2x-4y+13=0

directrix

x^{2} - 2 x - 4 y + 13 = 0

y = 2

Solution steps

Rewrite

x^{2} - 2 x - 4 y + 13 = 0

in the standard form

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

(h, k) = (1, 3), 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, 3)

y-coordinate

y = 3 - p

y = 3 - 1

Refine

y = 2

y = 18 x^{2} - 14 x + 9

y = + x^{2} - 3

x^{2} - 26 x + 65

y^{2} + 2 y + 1 = - 2 x + 4

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