What is the directrix x^2-6x-12y-51=0 ?

The directrix x^2-6x-12y-51=0 is y=-8

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

directrix x^2-6x-12y-51=0

directrix

x^{2} - 6 x - 12 y - 51 = 0

y = - 8

Solution steps

Rewrite

x^{2} - 6 x - 12 y - 51 = 0

in the standard form

4 \cdot 3 (y - (- 5)) = (x - 3)^{2}

(h, k) = (3, - 5), 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

(3, - 5)

y-coordinate

y = - 5 - p

y = - 5 - 3

Refine

y = - 8

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

- 8 x^{2}

y = + (x + 5)^{2} + 3

(y + 6)^{2} = \frac{15}{11} (x + 12)

(y + 6)^{2} = 9 (x - 1)