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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

foci

- \frac{1}{2} (x - 4)^{2} + 3

(4, \frac{5}{2})

Solution steps

Rewrite

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

in the standard form:

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

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

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

p

from the center

(4, 3)

along the y-axis

(4, 3 + p)

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

Refine

(4, \frac{5}{2})

(x - 6)^{2} = + 8 (y - 2)

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

(y - 2)^{2} + 16 (x - 3) = 0

z^{2} + 10 z + 5

x^{2} = 5 y