What is the directrix x^2+6x+8y=7 ?

The directrix x^2+6x+8y=7 is y=4

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directrix x^2+6x+8y=7

directrix

x^{2} + 6 x + 8 y = 7

y = 4

Solution steps

Rewrite

x^{2} + 6 x + 8 y = 7

in the standard form

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

(h, k) = (- 3, 2), p = - 2

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, 2)

y-coordinate

y = 2 - p

y = 2 - (- 2)

Refine

y = 4

y = x^{2} - 6 x - 1

y^{2} + 6 y + 8 x + 25 = 0

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

y = x^{2} + 2 x + 4

y = 5 x^{2}