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

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

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

directrix

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

x = 3 - \frac{k}{4}

Solution steps

Rewrite

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

in the standard form:

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

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

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

(3, 2)

x-coordinate

x = 3 - p

x = 3 - \frac{k}{4}

y = - 5 (x - 4)^{2} + 180

x^{2} - 2 x + 2

- x^{2} - 3 x - 2

y = x^{2} + 7 x - 3

y^{2} + 12 x - 2 y - 11 = 0