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

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

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

directrix

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

x = - \frac{5}{2}

Solution steps

Rewrite

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

in the standard form:

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

(h, k) = (- 2, 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

(- 2, 3)

x-coordinate

x = - 2 - p

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

Refine

x = - \frac{5}{2}

y = 5 x^{2} + 1

y = x^{2} + 9 x + 4

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

3 x^{2} + 4

3 x^{2} + 2