What is the directrix y=x^2+8x+18 ?

The directrix y=x^2+8x+18 is y= 7/4

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directrix y=x^2+8x+18

directrix

y = x^{2} + 8 x + 18

y = \frac{7}{4}

Solution steps

Rewrite

y = x^{2} + 8 x + 18

in the standard form

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

(h, k) = (- 4, 2), 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

(- 4, 2)

y-coordinate

y = 2 - p

y = 2 - \frac{1}{4}

Refine

y = \frac{7}{4}

y^{2} = x + 1

y = \frac{x ^{4} - 1}{x ^{2} - 1}

(x - 2) (x + 1)

5 x^{2} + 30 x + 24 y = 51

x^{2} - 2 x - 4 y + 9 = 0