Suppose that a parametric curve C is given by the equations x = f (t), y = g(t) for0 ≤ t ≤ 1 Find parametric equations for C that reverse the direction the curve is tracedas the parameter increases from 0 to 1
Question
Suppose that a parametric curve C is given by the equations x = f (t), y = g(t) for0 ≤ t ≤ 1 Find parametric equations for C that reverse the direction the curve is tracedas the parameter increases from 0 to 1
Solution
To reverse the direction of the curve as the parameter increases from 0 to 1, we can simply reverse the order of the equations for x and y.
Let's denote the new parametric equations as x' = f'(t) and y' = g'(t).
To reverse the direction, we can define x' as x' = f(1-t) and y' as y' = g(1-t).
Therefore, the parametric equations for C that reverse the direction of the curve as the parameter increases from 0 to 1 are x' = f(1-t) and y' = g(1-t).
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