What is the directrix y= 1/14 x^2+2 ?

The directrix y= 1/14 x^2+2 is y=-3/2

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directrix y= 1/14 x^2+2

directrix

y = \frac{1}{14} x^{2} + 2

y = - \frac{3}{2}

Solution steps

Rewrite

y = \frac{1}{14} x^{2} + 2

in the standard form:

4 \cdot \frac{7}{2} (y - 2) = (x - 0)^{2}

(h, k) = (0, 2), p = \frac{7}{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

(0, 2)

y-coordinate

y = 2 - p

y = 2 - \frac{7}{2}

Refine

y = - \frac{3}{2}

x^{2} - 4 x + 4

6 x^{2} + 12 x

3 x^{2} + 18

(x - 2)^{2} = - 12 (y - 4)

\frac{5 t ^{2}}{2}