What is the directrix x^2+2x-8y+33=0 ?

The directrix x^2+2x-8y+33=0 is y=2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

directrix x^2+2x-8y+33=0

directrix

x^{2} + 2 x - 8 y + 33 = 0

y = 2

Solution steps

Rewrite

x^{2} + 2 x - 8 y + 33 = 0

in the standard form

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

(h, k) = (- 1, 4), 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

(- 1, 4)

y-coordinate

y = 4 - p

y = 4 - 2

Refine

y = 2

6 x^{2} - 6 x

(x - \frac{5}{2})^{2} = 7 (y + 3.75)

y = - x^{2} + 8 x - 18

11 x^{2} - 8

y = 7 x^{2} + 5