Different Parametric eqs of Line

Discussion in 'Homework Help' started by zulfi100, Dec 14, 2013.

  1. zulfi100

    Thread Starter Member

    Jun 7, 2012
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  2. WBahn

    Moderator

    Mar 31, 2012
    17,748
    4,796
    A parametric equation is simply one in which the two coordinates (or how ever many there are for the number of dimensions) are functions of non-coordinate variables.

    So unstead of

    y = f(x)

    you have

    x = f(a,b,c)
    y = g(a,b,c)

    Not surprisingly, curves of different shape will have defining functions of different forms.

    Your first one

    x=x1+rcosθ, y=y1+rsinθ

    Is a circle of radius 'r' centered on the point <x1,y1>.

    Your second example is a straight line that goes from P1 to P2 as t goes from 0.0 to 1.0. The rest of the line is generated as t is allowed to go from -∞ to +∞.

    The next two equations appear to simply break out the vector P into separate <x,y> components.
     
  3. studiot

    AAC Fanatic!

    Nov 9, 2007
    5,005
    513
    Yes this is true of many curves or functions.

    Often there is a trigonometric parametric representation and an algebraic one, sometimes more than that.

    This trick is to choose the most appropriate for your purposes, not to convert one into the other.
     
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