What is the directrix y^2-6x-y+11=0 ?

The directrix y^2-6x-y+11=0 is x= 7/24

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

directrix y^2-6x-y+11=0

directrix

y^{2} - 6 x - y + 11 = 0

x = \frac{7}{24}

Solution steps

Rewrite

y^{2} - 6 x - y + 11 = 0

in the standard form

4 \cdot \frac{3}{2} (x - \frac{43}{24}) = (y - \frac{1}{2})^{2}

(h, k) = (\frac{43}{24}, \frac{1}{2}), p = \frac{3}{2}

Parabola is symmetric around the x-axis and so the directrix is a line parallel to the y-axis, a distance

- p

from the center

(\frac{43}{24}, \frac{1}{2})

x-coordinate

x = \frac{43}{24} - p

x = \frac{43}{24} - \frac{3}{2}

Refine

x = \frac{7}{24}

4 (x + 1)^{2}

x^{2} + 5 x - 24

\frac{1}{24} y^{2}

y = 25 x^{2} - 70 x + 36

- 3 x^{2} + 5 x