What is the directrix y^2-6x+6y+15=0 ?

The directrix y^2-6x+6y+15=0 is x=-1/2

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directrix y^2-6x+6y+15=0

directrix

y^{2} - 6 x + 6 y + 15 = 0

x = - \frac{1}{2}

Solution steps

Rewrite

y^{2} - 6 x + 6 y + 15 = 0

in the standard form

4 \cdot \frac{3}{2} (x - 1) = (y - (- 3))^{2}

(h, k) = (1, - 3), p = \frac{3}{2}

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, - 3)

x-coordinate

x = 1 - p

x = 1 - \frac{3}{2}

Refine

x = - \frac{1}{2}

y = - 0.005 x^{2} + x + 5

y = x^{2} - 9 x + 3

- 2 x^{2} - 24 x - 54

x^{2} - 2 x - 3

y = (3 x - 7)^{2}