Question

I'm not clear how to 'complete the square' with the equation x=y^2. Help? I need to do this to find the directrix and focus. Clearly the vertex is (0,0) but that is all I can figure out. Thanks! :D

Answer 1

Hello, Cecil-Weasel. Pop goes the weasel.

"I'm not clear how to 'complete the square' with the equation x=y^2" Cecil, you don't need to complete the square here, since y^2 is in itself a perfect square.

I take it you are to find the vertex, the focus and the directrix. Have you found these before, in other problems?

Answer 2

Yes, it takes me a while but I can usually get it. I think the trouble here is that the equation is not set up as x=ay^2+by+c. Instead it is missing a b(y). I feel that it should be easier but I'm not sure where to start.

Answer 3

I'll drop you some hints. This is a horizontal parabola; it opens to the right.

Let p be the positive distance from the vertex to the focus in such a horiz. parab.

The general equation for such a parab. is 4px=y^2.

Reference: http://colalg.math.csusb.edu/~devel/precalcdemo/conics/src/parabola.html

Suppose y=1. What would x be? Start with x=y^2.

Answer 4

@Cecil_the_Weasel ? Awaiting your response.

Answer 5

Hmm... I'm still having trouble setting up the problem. @mathmale

Answer 6

You were given x=y^2. You've correctly figured that the vertex is at (0,0).
Suppose I arbitrarily gave you y=1. What would x be in this case?

Answer 7

Also 1

Answer 8

Correct. Now, another form of the equation for this horiz. parab. is 4px=y^2.

Start with the coordinates of the point (1,1). Subs. x=1 and y=1 into the above eq'n. calculate p.

Answer 9

p= 1/4

Answer 10

Oh!
So would that be the focus? (If I switched the x and y again to make it horizontal) @mathmale

Answer 11

p=1/4 is not so much the focus as it is the distance from vertex to focus.
p is also the distance from vertex to directrix.
What is the eq'n of the directrix for this horiz. parab.?

Answer 12

x=-.25?

Answer 13

Yes, or x=-1/4. Very good!

Answer 14

Focus?

Answer 15

The value p in this situation would be the value of the focus in this particular problem because the focus is zero. I see now. Thank you very much :D

Answer 16

*the orgin is zero whoops

Answer 17

silly me

Answer 18

Actually, p represents a distance; the focus is written as (1/4, 0). No, not silly you. ;)

Answer 19

Thanks again :D I won't fail my test haha!

Answer 20

Hope not! Come back another time. Bye!