What is the directrix (x-5)^2=20(y-5) ?

The directrix (x-5)^2=20(y-5) is y=0

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directrix (x-5)^2=20(y-5)

directrix

(x - 5)^{2} = 20 (y - 5)

y = 0

Solution steps

Rewrite

(x - 5)^{2} = 20 (y - 5)

in the standard form:

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

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

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

(5, 5)

y-coordinate

y = 5 - p

y = 5 - 5

Refine

y = 0

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

x = + \frac{17}{4} (y + 2)^{2}

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

(x - 2)^{2} = 12 (y - 1)

y = x^{2} - 4 x + 9