What is the standard form of the equation of the parabola with a directrix at x=5 and a focus at (11,-7)?

1 Answer
May 22, 2016

(y+7)^2=12*(x-8)

Explanation:

Your equation is of the form

(y-k)^2=4*p*(x-h)

The focus is (h+p, k)

The directrix is (h-p)

Given the focus at (11,-7) -> h+p= 11 " and " k=-7

The directrix x=5 -> h-p = 5

h+p= 11" " (eq. 1)"
h-p =5 " " (eq. 2)

ul("use (eq. 2) and solve for h")

" " h=5+p" (eq. 3)"

ul("Use (eq. 1) + (eq. 3) to find the value of " p)

(5+p)+p=11

5+2p=11

2p=6

p=3

ul("Use (eq.3) to find the value of " h )

h=5+p

h=5+3

h=8

"Plugging the values of " h, p " and " k " in the equation "(y-k)^2=4*p*(x-h) " gives"

(y-(-7))^2=4*3*(x-8)

(y+7)^2=12*(x-8)