What is the foci (x^5+x^4+x^3+x^2+x+1)/(x^3+1) ?

The foci (x^5+x^4+x^3+x^2+x+1)/(x^3+1) is (-1/2 ,1)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

foci (x^5+x^4+x^3+x^2+x+1)/(x^3+1)

foci

\frac{x ^{5} + x ^{4} + x ^{3} + x ^{2} + x + 1}{x ^{3} + 1}

(- \frac{1}{2}, 1)

Solution steps

Rewrite

y = \frac{x ^{5} + x ^{4} + x ^{3} + x ^{2} + x + 1}{x ^{3} + 1}

in the standard form

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

(h, k) = (- \frac{1}{2}, \frac{3}{4}), p = \frac{1}{4}

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

p

from the center

(- \frac{1}{2}, \frac{3}{4})

along the y-axis

(- \frac{1}{2}, \frac{3}{4} + p)

= (- \frac{1}{2}, \frac{3}{4} + \frac{1}{4})

Refine

(- \frac{1}{2}, 1)

y^{2} - 12 y + 4 x + 4 = 0

x^{2} = - 20 y

x^{2} = - 36 y

y = 64 - x^{2}

x^{2} - 10 y - 4 x - 6 = 0

What is the foci (x^5+x^4+x^3+x^2+x+1)/(x^3+1) ?
The foci (x^5+x^4+x^3+x^2+x+1)/(x^3+1) is (-1/2 ,1)