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

The directrix (y-2)^2=-x-3 is x=-11/4

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

directrix

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

x = - \frac{11}{4}

Solution steps

Rewrite

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

in the standard form:

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

(h, k) = (- 3, 2), p = - \frac{1}{4}

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 - (- \frac{1}{4})

Refine

x = - \frac{11}{4}

2 x^{2} (2 + 1)

y = x^{2} + 16 x + 64

(x - 6)^{2} = 8 (y + 4)

y = - 3 x^{2} - 42 x - 22

+ (x - 2) = 3 (y - 5)^{2}