What is the directrix-x^2-4x+1 ?

The directrix-x^2-4x+1 is y= 21/4

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

directrix-x^2-4x+1

directrix

- x^{2} - 4 x + 1

y = \frac{21}{4}

Solution steps

Rewrite

y = - x^{2} - 4 x + 1

in the standard form

4 (- \frac{1}{4}) (y - 5) = (x - (- 2))^{2}

(h, k) = (- 2, 5), p = - \frac{1}{4}

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, 5)

y-coordinate

y = 5 - p

y = 5 - (- \frac{1}{4})

Refine

y = \frac{21}{4}

y - 7 = \frac{1}{24} (x + 4)^{2}

4 x^{2} - 24 x - 30

- y^{2} = 6 y + x

x = - \frac{1}{20} (y + 6)^{2} - 7

\frac{y ^{2} + 12 y + 36}{60}