What is the directrix 1/4 (y+3)=(x-2)^2 ?

The directrix 1/4 (y+3)=(x-2)^2 is y=-49/16

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directrix 1/4 (y+3)=(x-2)^2

directrix

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

y = - \frac{49}{16}

Solution steps

Rewrite

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

in the standard form:

4 \cdot \frac{1}{16} (y - (- 3)) = (x - 2)^{2}

(h, k) = (2, - 3), p = \frac{1}{16}

Parabola is symmetric around the y-axis and so the directrix is a line parallel to the x-axis, a distance

- p

from the center

(2, - 3)

y-coordinate

y = - 3 - p

y = - 3 - \frac{1}{16}

Refine

y = - \frac{49}{16}

x = - 2 y^{2}

x^{2} + y^{2} = 36

\frac{x ^{2}}{7} + \frac{y ^{2}}{16} = 1

y^{2} = \frac{7}{2} x

x^{2} = - 8 y

What is the directrix 1/4 (y+3)=(x-2)^2 ?
The directrix 1/4 (y+3)=(x-2)^2 is y=-49/16