What is the directrix x^2+2x-y=3 ?

The directrix x^2+2x-y=3 is y=-17/4

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

directrix x^2+2x-y=3

directrix

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

y = - \frac{17}{4}

Solution steps

Rewrite

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

in the standard form

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

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

(- 1, - 4)

y-coordinate

y = - 4 - p

y = - 4 - \frac{1}{4}

Refine

y = - \frac{17}{4}

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

25 x^{2} - 70 x + 36

y = x^{2} - 5 x - 6

y^{2} + 8 y + 4 x + 20 = 0

- x^{2} + 4