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

The directrix y=-1/14 x^2+2 is y= 11/2

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directrix y=-1/14 x^2+2

directrix

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

y = \frac{11}{2}

Solution steps

Rewrite

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

in the standard form:

4 (- \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{11}{2}

2 y^{2} = 16 x

y^{2} + 8 x + 2 y + 33 = 0

2 x^{2} - x + 1

y^{2} = x

20 x = y^{2}