What is the directrix (y+2)^2=-4(x-3) ?

The directrix (y+2)^2=-4(x-3) is x=4

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directrix (y+2)^2=-4(x-3)

directrix

(y + 2)^{2} = - 4 (x - 3)

x = 4

Solution steps

Rewrite

(y + 2)^{2} = - 4 (x - 3)

in the standard form:

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

(h, k) = (3, - 2), p = - 1

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, - 2)

x-coordinate

x = 3 - p

x = 3 - (- 1)

Refine

x = 4

5 x^{2} - 15 x + 3

x^{2} + 10 x - 24

x (4 - x)

5 x^{2} - 3 x + 3

y = (x - 3)^{2} + 4