What is the directrix x=-1/2 (y+3)^2+1 ?

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

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directrix x=-1/2 (y+3)^2+1

directrix

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

x = \frac{3}{2}

Solution steps

Rewrite

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

in the standard form:

4 (- \frac{1}{2}) (x - 1) = (y - (- 3))^{2}

(h, k) = (1, - 3), 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

(1, - 3)

x-coordinate

x = 1 - p

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

Refine

x = \frac{3}{2}

x^{2} + y^{2} = 121

\frac{x ^{2}}{9} + \frac{y ^{2}}{25} = 1

x^{2} = 2 y

\frac{x ^{2}}{49} - \frac{y ^{2}}{16} = 1

y^{2} = 12 x

What is the directrix x=-1/2 (y+3)^2+1 ?
The directrix x=-1/2 (y+3)^2+1 is x= 3/2