1. ## parable

To determine the equation of the parable whose string minimum joining the focal points A(3,5) and B(3,-3)

$y^2-2y-8x+9=0$ and $y^2-2y+8x-39=0$

2. OK, to get started here, list off things you know about focal points of parabolas.

3. I construct parables and the vertex, focus and $\frac{p}{2}$. Now with points I do not understand

4. OK.
Explain what a string minimum means.
The more clear you are, the more helpful I can be.

5. rope focal minimum joining the points

Sorry is that I am Brazilian and I do not understand English very well

6. Originally Posted by Apprentice123
To determine the equation of the parable whose string minimum joining the focal points A(3,5) and B(3,-3)

$y^2-2y-8x+9=0$ and $y^2-2y+8x-39=0$
A parabola only has one focal point ..... A(3,5) and B(3,-3) cannot both be focal points of the parabola.

Are you trying to find the equation of two parabolas:

Parabola 1 has focal point A(3,5).

Parabola 2 has focal point B(3,-3).

But I don't understand the 'string minimum' condition you talk about. Are you minimising some sort of distance between these two parabolas and their focal points?

7. No. I need find the equation of the parable in which the rope focal joins the points A and B

8. Alright, hold on a second. Mr. Fantastic corrected me on some little thing, so I want to feel really good that I got this right.
I think.

OK, I started drawing a diagram of the two points. Then, I drew the line segment between them. Then, I found the midpoint. If I cheat ahead an look at the answer, I find that the midpoint between the two points is the focus of both parabolas. Also, the two points given lie on both parabolas.
Now, I am going to conjecture here a bit. I think that what you need to find are the possible equations of parabolas such that the focus is the minimum distance from both points. If you do this and follow the steps laid out in the other parabola help topic, I think you should come up with the right answer.

9. Originally Posted by bleesdan
Alright, hold on a second. Mr. Fantastic corrected me on some little thing, so I want to feel really good that I got this right.
I think.

OK, I started drawing a diagram of the two points. Then, I drew the line segment between them. Then, I found the midpoint. If I cheat ahead an look at the answer, I find that the midpoint between the two points is the focus of both parabolas. Also, the two points given lie on both parabolas.
Now, I am going to conjecture here a bit. I think that what you need to find are the possible equations of parabolas such that the focus is the minimum distance from both points. If you do this and follow the steps laid out in the other parabola help topic, I think you should come up with the right answer.
Thankyou for saving me the trouble of confirming my hunch.