What is the directrix x^2-6x-y+33=0 ?

The directrix x^2-6x-y+33=0 is y= 95/4

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directrix x^2-6x-y+33=0

directrix

x^{2} - 6 x - y + 33 = 0

y = \frac{95}{4}

Solution steps

Rewrite

x^{2} - 6 x - y + 33 = 0

in the standard form

4 \cdot \frac{1}{4} (y - 24) = (x - 3)^{2}

(h, k) = (3, 24), p = \frac{1}{4}

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

(3, 24)

y-coordinate

y = 24 - p

y = 24 - \frac{1}{4}

Refine

y = \frac{95}{4}

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

y = - \frac{1}{12} x^{2}

\frac{40 x ^{3}}{3 x}

(x - 3)^{2} = - 4 (y + 1)

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