What is the directrix (y+6)^2=9(x-1) ?

The directrix (y+6)^2=9(x-1) is x=-5/4

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directrix (y+6)^2=9(x-1)

directrix

(y + 6)^{2} = 9 (x - 1)

x = - \frac{5}{4}

Solution steps

Rewrite

(y + 6)^{2} = 9 (x - 1)

in the standard form:

4 \cdot \frac{9}{4} (x - 1) = (y - (- 6))^{2}

(h, k) = (1, - 6), p = \frac{9}{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

(1, - 6)

x-coordinate

x = 1 - p

x = 1 - \frac{9}{4}

Refine

x = - \frac{5}{4}

y^{2} + 10 x = 0

y = - \frac{1}{2} (x + 6)^{2} + 8

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

y = 5 x^{2} + 1

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