What is the foci 3x^2-16x+5 ?

The foci 3x^2-16x+5 is (8/3 ,-65/4)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

foci 3x^2-16x+5

foci

3 x^{2} - 16 x + 5

(\frac{8}{3}, - \frac{65}{4})

Solution steps

Rewrite

y = 3 x^{2} - 16 x + 5

in the standard form

4 \cdot \frac{1}{12} (y - (- \frac{49}{3})) = (x - \frac{8}{3})^{2}

(h, k) = (\frac{8}{3}, - \frac{49}{3}), p = \frac{1}{12}

Parabola is symmetric around the y-axis and so the focus lies a distance

p

from the center

(\frac{8}{3}, - \frac{49}{3})

along the y-axis

(\frac{8}{3}, - \frac{49}{3} + p)

= (\frac{8}{3}, - \frac{49}{3} + \frac{1}{12})

Refine

(\frac{8}{3}, - \frac{65}{4})

y^{2} - 12 y + 6 x + 36 = 0

x^{2} - 6 x - 20 y - 11 = 0

y = 3 x^{2} - 36 x + 81

(y - 6)^{2}

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