What is the directrix (x-3)^2=8(y-5) ?

The directrix (x-3)^2=8(y-5) is y=3

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directrix (x-3)^2=8(y-5)

directrix

(x - 3)^{2} = 8 (y - 5)

y = 3

Solution steps

Rewrite

(x - 3)^{2} = 8 (y - 5)

in the standard form:

4 \cdot 2 (y - 5) = (x - 3)^{2}

(h, k) = (3, 5), p = 2

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

(3, 5)

y-coordinate

y = 5 - p

y = 5 - 2

Refine

y = 3

y = \frac{x ^{2} x ^{1}}{x}

3 - x^{2}

y = 3 - x^{2}

y = 1 - x - x^{2}

- \frac{( x + 3 ) ^{2}}{20} + 1