Question

Use the distance formula to find the equation of a parabola with focus (-3, 0) and directrix x = 6.
Thanks!

Answer 1

I got lost at (

Answer 2

by definition of a parabola,
it is the locus of points that are equidistant from the focus and the directrix.

let (x,y) be a point on the parabola

1) its distance from (-3,0)
\(=\sqrt{[x-(-3)]^2+(y-0)^2}\)

2) its distance from the directrix x=6
\(\Large=\frac{|x+6|}{1}=|x+6|\)

by definition, they are equal!

Answer 3

\[
|x+6|=\sqrt{(x+3)^2+y^2}
\]
square both sides and simplify

Answer 4

correction...
it should be :
\[|x-6|=\sqrt{(x+3)^2+y^2}\]

Answer 5

and evaluate

Answer 6

Okay... so, For the first part, I got -36, I don't think I understand how to do everthing under the square root sign.

Answer 7

@electrokid

Answer 8

just the 36?
you are supposed to get an equation.
it should look like

x=..... something in "y" and a constant term

Answer 9

Yeah, I did the absolute value stuff first @electrokid

Answer 10

how?

Answer 11

you can take a picture of your work and post it here so I see

Answer 12

-6 square rooted... WAIT wouldn't it be 36 not -36?

Answer 13

I do not follow your statement.
use the equation editor below to write what you did

Answer 14

how did you get rid of the "absolute value" sign?

Answer 15

\[|x-6| =x-6 which is 36\]

Answer 16

but we do not have the "x"

Answer 17

what formula or property did you use ?

Answer 18

Nope its -36. you cant get rid of the sigh if its negative

Answer 19

the only way to get rid of an absolute value sign is
1) by squaring it
OR
2) by writing two possible results

Answer 20

since we want only one equation, we square it
so, we expand
\[(x-6)^2\]

Answer 21

Oh okay

Answer 22

what do we get for the expansion?