What is the foci+(y^3-100y)/(y+10) ?

The foci+(y^3-100y)/(y+10) is (-99/4 ,5)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

foci+(y^3-100y)/(y+10)

foci

+ \frac{y ^{3} - 100 y}{y + 10}

(- \frac{99}{4}, 5)

Solution steps

Rewrite

x = \frac{y ^{3} - 100 y}{y + 10}

in the standard form

4 \cdot \frac{1}{4} (x - (- 25)) = (y - 5)^{2}

(h, k) = (- 25, 5), p = \frac{1}{4}

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

p

from the center

(- 25, 5)

along the x-axis

(- 25 + p, 5)

= (- 25 + \frac{1}{4}, 5)

Refine

(- \frac{99}{4}, 5)

x^{2} - 10 x - 24 y = - 25 - 24

x^{2} = 8 (y - 2)

x^{2} - 2 x + 5

(y - 2)^{2} = 8 (x - 5)

(x + 1)^{2} = (y + 4)