MATH 32A Lecture Notes - Lecture 5: Parametric Equation, Unit Vector, Farad
Document Summary
You can isolate the t in each equation so that the expression with x is equal to the expression with y, then rearrange the equations so you get y=f(x). This is equivalent to giving the pair of functions x(t), y(t) separately. This is called parametric equation, t is called the parameter. In 3-d it can be r(t) = . As t increases, position on graph moves in a certain direction. There are many (infinitely many) ways to parametrize any given curve. Many vector-valued functions that can represent the same curve. Examples: x = t and y = t 2 r(t) = y = x 2 . Also: x = e t and y = e 2t would also give you y = x 2 . Given a vector-valued function or a set of parametric equations, combine it into single equation by eliminating the ts. Solve one equation for t and substitte into another.