What is the directrix x=2y^2-1-(5y-6) ?

The directrix x=2y^2-1-(5y-6) is x= 7/4

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

directrix x=2y^2-1-(5y-6)

directrix

x = 2 y^{2} - 1 - (5 y - 6)

x = \frac{7}{4}

Solution steps

Rewrite

x = 2 y^{2} - 1 - (5 y - 6)

in the standard form

4 \cdot \frac{1}{8} (x - \frac{15}{8}) = (y - \frac{5}{4})^{2}

(h, k) = (\frac{15}{8}, \frac{5}{4}), p = \frac{1}{8}

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{15}{8}, \frac{5}{4})

x-coordinate

x = \frac{15}{8} - p

x = \frac{15}{8} - \frac{1}{8}

Refine

x = \frac{7}{4}

x^{2} - 2 x - 4 y + 13 = 0

y = 18 x^{2} - 14 x + 9

y = + x^{2} - 3

x^{2} - 26 x + 65

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