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

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

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

directrix

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

x = - \frac{3}{2}

Solution steps

Rewrite

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

in the standard form:

4 (- \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{3}{2}

y = (x + 314)^{2}

y = x^{2} - 13 x + 40

(x + 2)^{2} = - 8 (y - 1)

\frac{x ( x + 5 )}{7}

y = + x^{2} - 18 x + 73