What is the directrix x^2+2x-12y+37=0 ?

The directrix x^2+2x-12y+37=0 is y=0

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directrix x^2+2x-12y+37=0

directrix

x^{2} + 2 x - 12 y + 37 = 0

y = 0

Solution steps

Rewrite

x^{2} + 2 x - 12 y + 37 = 0

in the standard form

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

(h, k) = (- 1, 3), p = 3

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

(- 1, 3)

y-coordinate

y = 3 - p

y = 3 - 3

Refine

y = 0

2 x^{2} + 16 x + 35

y = 40 x - 5 x^{2}

4 y^{2} + 3 x = 0

(x - 1)^{2} = y - 2

x^{2} - 4 x + 2