What is the directrix y^2+6y+2x+1=0 ?

The directrix y^2+6y+2x+1=0 is x= 9/2

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directrix y^2+6y+2x+1=0

directrix

y^{2} + 6 y + 2 x + 1 = 0

x = \frac{9}{2}

Solution steps

Rewrite

y^{2} + 6 y + 2 x + 1 = 0

in the standard form

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

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

(4, - 3)

x-coordinate

x = 4 - p

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

Refine

x = \frac{9}{2}

y = x^{2} - 7

2 x - 5 x^{2}

y^{2} - 6 x - 6 y + 3 = 0

y = 3 x^{2} - 31 x + 56 - (x - 8)

x^{2} - 5 x + 6