Standard form of the equation of parabola

Click For Summary

Homework Help Overview

The problem involves writing the equation in standard form for a parabola with a specified axis of symmetry and focus. The axis of symmetry is given as y=0, indicating a horizontal orientation, and the focus is located at (-5,0).

Discussion Character

  • Exploratory, Conceptual clarification, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the form of the parabola's equation, with some suggesting it may be in the form of ax^2 + bx + c, while others argue that the correct form should reflect the horizontal orientation, possibly x = ay^2 + by + c. There is also mention of the relationship between the focus, vertex, and axis of symmetry.

Discussion Status

The discussion is ongoing, with participants seeking clarification on how to approach the problem. Some have requested examples to guide their understanding, while others are exploring the implications of the given conditions.

Contextual Notes

Participants express difficulty in finding relevant examples in their textbooks and indicate a lack of familiarity with conic sections, which adds to the complexity of the discussion.

jOANIE
Messages
6
Reaction score
0

Homework Statement



Write the equation in standard form for the parabola with an axis of symmetry y=0 and focus(-5,0).

Homework Equations


I think ax^2+bx+c. Also maybe x = -b/2a. But I don't know how to apply these.



The Attempt at a Solution


I know that focus and vertex lie on axis of symmetry and that directrix ane axis of symmetry are perpendicular to each other.

If you could give me a similar example worked out, I would be able to do this one. Thanks.
 
Physics news on Phys.org
jOANIE said:

Homework Statement



Write the equation in standard form for the parabola with an axis of symmetry y=0 and focus(-5,0).

Homework Equations


I think ax^2+bx+c.
I think not. First off, that's not an equation. Second, the axis of symmetry is the line y = 0 (the x-axis). This means that the equation will be x = ay^2 + by + c.
jOANIE said:
Also maybe x = -b/2a. But I don't know how to apply these.
x = -b/(2a) isn't the equation of a parabola; it gives you the x-coordinate of the vertex for a parabola that opens up or down. Your parabola opens left or right.
jOANIE said:

The Attempt at a Solution


I know that focus and vertex lie on axis of symmetry and that directrix ane axis of symmetry are perpendicular to each other.

If you could give me a similar example worked out, I would be able to do this one. Thanks.

Based on the information you provided, there are an infinite number of parabolas that satisfy these conditions. Aren't there any examples showing how to do this in your textbook?
 
Hello--Thanks for responding. I cannot find an example like this one in my book. Could you give me any hints on how to begin this problem? I am completely self-taught in math and am trying to understand conics, which I have not attempted before. I am also good at following examples and, actually, learn quite a bit from them.
 
OK, what's the example that seems the closest? Are there any examples where you're supposed to find the equation of a parabola of any kind? Maybe we can help you make some connections.
 

Similar threads

  • · Replies 4 ·
Replies
4
Views
2K
  • · Replies 44 ·
2
Replies
44
Views
4K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 3 ·
Replies
3
Views
3K
Replies
9
Views
2K
  • · Replies 16 ·
Replies
16
Views
2K
  • · Replies 40 ·
2
Replies
40
Views
9K
  • · Replies 1 ·
Replies
1
Views
3K
  • · Replies 5 ·
Replies
5
Views
2K
  • · Replies 1 ·
Replies
1
Views
2K