What is the directrix x^2+a ?

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directrix x^2+a

directrix

x^{2} + a

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

Solution steps

Rewrite

y = x^{2} + a

in the standard form:

4 \cdot \frac{1}{4} (y - a) = (x - 0)^{2}

(h, k) = (0, a), 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

(0, a)

y-coordinate

y = a - p

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

y = - \frac{1}{4} (x^{2} - 14 x + 13)

x^{2} + 5

y^{2} = - 32 x

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

y = - 8 x^{2} + 4