Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Equation of a parabola

  1. Sep 11, 2014 #1
    The general equation of a parabola is:
    (y - y1) = A(x - x1)^2

    A is the scaling factor
    y1 is the y coordinate of a vertex/point on the parabola
    x1 is the x coordinate of a vertex/point on the parabola

    My two questions are:
    1. Can (x,y) be any point on the graph ?
    2. If so, then if x - x1 = 0 and y- y1 = 0 (if the difference between the points are 0) then does that mean the point (x,y) is on the parabola?
     
  2. jcsd
  3. Sep 11, 2014 #2

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Yes, (x, y) refers to any point on the parabola.

    Your question is a little confusing (or confused). Again, (x, y) can refer to any point on the parabola. "if x- x1= 0 and y- y1= 0" then x= x1 and y= y1 is a specific point on the parabola. In fact, it is the vertex of the parabola- the lowest point if A is positive, highest point if A is negative.
     
  4. Sep 11, 2014 #3

    SteamKing

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper

    That's what the equations of these curves are for.

    Instead of having to compile a list of the infinite number of point coordinates which fall on the curve, a simple equation can be used to generate one point or many points, all of which will fall on the curve

    Any point (x,y) which satisfies the equation of the parabola is a point on that parabola.

    Now, why all of this confusion?
     
  5. Sep 11, 2014 #4

    Integral

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    I would say that (x,y) is some point in the x,y plane, may on the parabola maybe not.

    Points on a parabola are given by: (x, (x-x1)2+ y1))
     
  6. Sep 12, 2014 #5

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    In the original post the reference was to (x, y) satisfying the equation [itex](y- y_1)= A(x- x_1)^2[/itex].

    Those (x, y) are points on the parabola, not arbitrary points in the plane.
     
  7. Sep 12, 2014 #6
    Thanks guys. So if (x,y) = (x1,y1), then this satisfies the parabola equation and (x1,y1) is the vertex?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Equation of a parabola
  1. Equation of a parabola (Replies: 1)

Loading...