What is the directrix x^2-2x+8y+9=0 ?

The directrix x^2-2x+8y+9=0 is y=1

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directrix x^2-2x+8y+9=0

directrix

x^{2} - 2 x + 8 y + 9 = 0

y = 1

Solution steps

Rewrite

x^{2} - 2 x + 8 y + 9 = 0

in the standard form

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

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

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, - 1)

y-coordinate

y = - 1 - p

y = - 1 - (- 2)

Refine

y = 1

\frac{1}{20} x^{2}

+ t^{2}

y^{2} - 4 x = 0

x^{2} - 6

4 x^{2} + 3 x - 1