Question

Help with Parabolas

Answer 1

Find the directrix of the following parabola:

(x − 1)2 + 8(y + 2) = 0

Answer 2

2x-2+8y + 16=0

Answer 3

Combine like terms first :)

Answer 4

2x + 8y + 14=0

Answer 5

I'll let campbell finish and explain it to you.... :) good luck!

Answer 6

well if you re-write the equation as

\[(x - 1)^2 = -8(y +2)\]

the standard form is

\[(x - h)^2 = 4a(y - k)\]

the vertex is at (h, k)

and the equation of the dirctrix is y = k - a

so find a and k... what do you think they are..?

Answer 7

oops, forgot to say, a is the focal length, the distance between the vertex and focus

it is also the distance the directrix is from the vertex

Answer 8

question to flip 8(y+8) would you subtract it or divide it to get it to the otehr side of the equation?

Answer 9

by comparing it to the standard form I wrote, there is no need to expand. its just identifying and then a simple calculation

Answer 10

wait do you fill it in? s: This is my first time doing this. a is -8 same with y ? or do we have to solve to find each one?

Answer 11

4a = -8 so what is a..?

Answer 12

a=-2

Answer 13

next where is the vertex..?

a is correct

Answer 14

(-1 ,2)

Answer 15

close... h = 1 and k= -2

so the vertex is (1, -2)

the parabola is concave down... I know that after rewriting it...

the the equation of the directrix is y = -2 -a...

substitute your a value to find the equation

Answer 16

ohh its not negative one its just the standard form

Answer 17

ok i understand

Answer 18

y=-2 - (-2)?

Answer 19

-2+2 = 0?

Answer 20

yes to sthe directrix is y = 0