What is the directrix 9t-2t^2 ?

The directrix 9t-2t^2 is y= 41/4

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

directrix 9t-2t^2

directrix

9 t - 2 t^{2}

y = \frac{41}{4}

Solution steps

Rewrite

y = 9 t - 2 t^{2}

in the standard form

4 (- \frac{1}{8}) (y - \frac{81}{8}) = (t - \frac{9}{4})^{2}

(h, k) = (\frac{9}{4}, \frac{81}{8}), p = - \frac{1}{8}

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

(\frac{9}{4}, \frac{81}{8})

y-coordinate

y = \frac{81}{8} - p

y = \frac{81}{8} - (- \frac{1}{8})

Refine

y = \frac{41}{4}

x^{2} = 40 y

x^{2} - 6 x - y + 33 = 0

- 2 x^{2} + 4 x - 9

y = - \frac{1}{12} x^{2}

\frac{40 x ^{3}}{3 x}