What is the directrix x=-1/2 (y-4)^2+1/2 ?

The directrix x=-1/2 (y-4)^2+1/2 is x=1

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directrix x=-1/2 (y-4)^2+1/2

directrix

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

x = 1

Solution steps

Rewrite

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

in the standard form:

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

(h, k) = (\frac{1}{2}, 4), p = - \frac{1}{2}

Parabola is symmetric around the x-axis and so the directrix is a line parallel to the y-axis, a distance

- p

from the center

(\frac{1}{2}, 4)

x-coordinate

x = \frac{1}{2} - p

x = \frac{1}{2} - (- \frac{1}{2})

Refine

x = 1

y^{2} - 4 y - 8 x - 12 = 0

- (y + 3)^{2} - 1

7 x^{2} - 3 x + 10 - (- 4 x^{2} + 6 x - 4)

y = - 2 x^{2} + 64 x - 90

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

What is the directrix x=-1/2 (y-4)^2+1/2 ?
The directrix x=-1/2 (y-4)^2+1/2 is x=1