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

The directrix-2(x+3)=(y-1)^2 is x=-5/2

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

directrix

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

x = - \frac{5}{2}

Solution steps

Rewrite

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

in the standard form:

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

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

(- 3, 1)

x-coordinate

x = - 3 - p

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

Refine

x = - \frac{5}{2}

2 y^{2} = - 5 x

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

y = \frac{1}{4} x^{2} - \frac{5}{2} x + \frac{13}{4}

4 x^{2} - 25

y = - 6 x^{2} + 37 x + 13