# Different Parametric eqs of Line

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

Jun 7, 2012
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2. ### WBahn Moderator

Mar 31, 2012
23,847
7,378
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.

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.

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
5,003
522
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.