What is the directrix-12y+10=x^2-4x+14 ?

The directrix-12y+10=x^2-4x+14 is y=3

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directrix-12y+10=x^2-4x+14

directrix

- 12 y + 10 = x^{2} - 4 x + 14

y = 3

Solution steps

Rewrite

- 12 y + 10 = x^{2} - 4 x + 14

in the standard form

4 (- 3) (y - 0) = (x - 2)^{2}

(h, k) = (2, 0), 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

(2, 0)

y-coordinate

y = 0 - p

y = 0 - (- 3)

Refine

y = 3

- 2 x^{2} + 11

y = (x - 4) (x - 7)

y = - 2 x^{2} + 6

y = - 2 x^{2} + 7

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