What is the directrix (x-1)^2=-2y-11 ?

The directrix (x-1)^2=-2y-11 is y=-5

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directrix (x-1)^2=-2y-11

directrix

(x - 1)^{2} = - 2 y - 11

y = - 5

Solution steps

Rewrite

(x - 1)^{2} = - 2 y - 11

in the standard form:

4 (- \frac{1}{2}) (y - (- \frac{11}{2})) = (x - 1)^{2}

(h, k) = (1, - \frac{11}{2}), p = - \frac{1}{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, - \frac{11}{2})

y-coordinate

y = - \frac{11}{2} - p

y = - \frac{11}{2} - (- \frac{1}{2})

Refine

y = - 5

(x - 2)^{2} = 8 (y + 1)

y^{2} = 24 x

y = - \frac{( x + 3 ) ^{2}}{20} + 1

x^{2} - 6 x + 10

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