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

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

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

directrix

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

y = \frac{11}{4}

Solution steps

Rewrite

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

in the standard form:

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

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

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}{4}

Refine

y = \frac{11}{4}

y^{2} - 8 y + 4 x = 0

x^{2} + 4 x + 6 y - 2 = 0

48 x - 6 x^{2}

2 x^{2} - x

x^{2} = - 10 y