What is the directrix (y-2)^2=40(x-2) ?

The directrix (y-2)^2=40(x-2) is x=-8

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directrix (y-2)^2=40(x-2)

directrix

(y - 2)^{2} = 40 (x - 2)

x = - 8

Solution steps

Rewrite

(y - 2)^{2} = 40 (x - 2)

in the standard form:

4 \cdot 10 (x - 2) = (y - 2)^{2}

(h, k) = (2, 2), p = 10

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

(2, 2)

x-coordinate

x = 2 - p

x = 2 - 10

Refine

x = - 8

(x - 3)^{2} - 1

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

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

x^{2} + 16 x + 8

(x - 3)^{2} - 4