Question

quick question on focus parabola and the value of "p"

Answer 1

if we have the equation 6x-x^2=8y+1

i can get thsi to the form

-8(y-1)=(x-3)^2

vertex=(3,1)

Answer 2

focus is (h,k-p)? but isn't p here -2? it appears as if its 2 since the focus is suppose to be (3,-1)

Answer 3

but isn't -8/4=-2?

Answer 4

First, figure out whether this parabola is a vertical or horiz one, and whether it opens up, opens down, opens to the left or opens to the right.

Answer 5

Whether it's x that's squared, or y, decides whether the para. is vert. or horiz.

If vert, and if the para. opens up, the simplest equation involving p would be 4py=x^2.
If the vertex is not at (0,0), but at (h,k), the formula would be 4p(y-k)=(x-h)^2.

There's more to it than that, but this info may help you to get started.

Answer 6

im aware of all that. im just talking about solving for p

Answer 7

Sorry if it seems I'm overwhelming you with facts and appraoches. You do need to know what to do and where to start, right?

So, try to put into words what kind of guidance you need if you're "already aware of all that."

Answer 8

ok, in the equation i posted? is the value of p not -2?

Answer 9

i understand that it goes downwards and therefore the value of p does make more sense but my textbook does say a downward parabola goes by (h,p-k) in focus

Answer 10

*(h,k-p)

Answer 11

Your -8(y-1)=(x-3)^2 looks good. Compare this to:
4p(y-1)=(x-3)^2. Obviously 4p must = -8.

What is p?

Answer 12

-2

Answer 13

That's true. If p is neg then the parab. opens downward; if pos, the parab. opens upward.

Answer 14

what are the coordinates of the vertex? of the focus? What is the eq'n of the directrix?

Answer 15

vertex:3,1
focus:3,-1 but the focus equation of (h,k-p) says its 3,2
directrix is suppose to be y=3 but if p is -2, then the directrix equation of k+p says its -1

so i know the right answers but the equations in my textbooks keep tellin gme other wise

Answer 16

How do you "know" that you have the right answers?
One way would be to actually plot / graph the parabola, along with its focus and directrix.

Another would be to re-examine the question and what you've done so far:
if we have the equation 6x-x^2=8y+1

Answer 17

I know i have the right answers because ive checked my textbook answers and I know that in this equation since it is downwards, the focus's y coordinate must be less than the focus etc

Answer 18

*must be less than the vertex

Answer 19

I'd agree with that.

Answer 20

i guess its better to go by instinct and not a formula. if so then i think i got it

Answer 21

just not sure why my textbook would say the focus (h,k-P) for a downwards when a negative p makes it positive

Answer 22

I'd agree that your vertex is (3,1).

Given that the para. opens downward, what are the actual coordinates of the focus?

Answer 23

(3,-1)

Answer 24

But you said earlier: "vertex=(3,1)"

What about the focus?

Answer 25

Keep in mind that we've agreed that p=-2.

Answer 26

The focus is (3,-1)

Answer 27

Yes. Notice that all you had to do was to subtract -2 from the y-coord. of the vertex.

Now, what is the equation of the directrix of this parabola?

Answer 28

p is just the distance from the vertex to the focus. Often books use something like an absolute value sign to avoid confusion. p is never negative (negative just implies the direction of opening)

Don't memorize things like (h, k-p). Instead just graph the parabola, using the vertex and direction of opening, and you'll never need them. You'll find the focus by using the fact that p is the vertex to focus distance.

Graph hyperbolas and ellipses the same way. There's way too many formulas and such for those, that it's better to learn how to find the foci and asymptotes by graphing.

Answer 29

What I was looking for @agent0smith

thanks