how do you find the focus and the directrix line if all you have is the equation in parabolic form?

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- Apr 1st 2008, 06:42 PMdanielle1parabolas
how do you find the focus and the directrix line if all you have is the equation in parabolic form?

- Apr 1st 2008, 06:45 PMJhevon
see post #2 here

- Apr 1st 2008, 06:47 PMdanielle1
woah i have no idea where that p came from.

- Apr 1st 2008, 06:49 PMJhevon
- Apr 1st 2008, 06:53 PMdanielle1
ughh i wish my teacher would do his job. i have no idea what you mean. like if i have y=(x-2)+3, i know how to get the vertex but not the focus or the directrix

- Apr 1st 2008, 06:54 PMJhevon
- Apr 1st 2008, 06:58 PMdanielle1
wait.... what??? why not?

- Apr 1st 2008, 07:06 PMJhevon
the x is not squared. i suppose you meant to type

now, you should know that if a parabola is in the form , the vertex is given by ...oh, you do know that. ok, moving on.

now we want to get this parabola to look like the form i used in the post i directed you to.

the form must look like

in this form, the focus is:

and the directrix is:

now,

the coefficient of y is 1, so where would the 4 come from? well, we can notice that

thus, we have

so, we have ....look familiar? - Apr 1st 2008, 07:10 PMdanielle1
omg i think i actually get it now. thank you so much!

- Apr 1st 2008, 07:11 PMJhevon
- Apr 1st 2008, 07:23 PMdanielle1
hmm.. what do i do with the p again?

- Apr 1st 2008, 07:41 PMJhevon
- Apr 1st 2008, 07:43 PMdanielle1
k+p, but i don't know what to plug in for p

- Apr 1st 2008, 07:55 PMJhevon
it seems you are not reading through my posts. first of all, i never said anything was k + p. neither the focus nor the directrix is k + p. the focus is a coordinate and the directrix is a horizontal line.

i am sorry, but i really do not see the problem you are having. i went through the algebraic manipulations and tried to make it plain. but let's try again.

...........this is the form we want

....... ......... .......

............this is the form we got our equation in

now, the focus is:

and the directrix is:

can you tell me what h, p and k are? - Apr 1st 2008, 07:58 PMdanielle1
i meant k+p as the y coordinate. and i didn't realize that p is 1/4.... here i'll try again now