What is the directrix x=-1/2 (y-2)^2+5 ?

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

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directrix x=-1/2 (y-2)^2+5

directrix

x = - \frac{1}{2} (y - 2)^{2} + 5

x = \frac{11}{2}

Solution steps

Rewrite

x = - \frac{1}{2} (y - 2)^{2} + 5

in the standard form:

4 (- \frac{1}{2}) (x - 5) = (y - 2)^{2}

(h, k) = (5, 2), 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

(5, 2)

x-coordinate

x = 5 - p

x = 5 - (- \frac{1}{2})

Refine

x = \frac{11}{2}

y = 48 x - 8 x^{2}

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

y = - 2 x^{2}

y = 2 x^{2} - 3

(y + 1)^{2} = 16 (x - 3)

What is the directrix x=-1/2 (y-2)^2+5 ?
The directrix x=-1/2 (y-2)^2+5 is x= 11/2