What is the foci-3(x+1)^2-1 ?

The foci-3(x+1)^2-1 is (-1,-13/12)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

foci-3(x+1)^2-1

foci

- 3 (x + 1)^{2} - 1

(- 1, - \frac{13}{12})

Solution steps

Rewrite

y = - 3 (x + 1)^{2} - 1

in the standard form:

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

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

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

p

from the center

(- 1, - 1)

along the y-axis

(- 1, - 1 + p)

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

Refine

(- 1, - \frac{13}{12})

- 16 x + y^{2} + 2 y - 63 = 0

y = - x^{2} - 6 x + 15

(x + 3) + (y - 2)^{2} = 0

x = 2 y - y^{2}

- \frac{( x + 3 ) ^{2}}{20} + 1