HOW TO FIND WHERE THE GRAPH OF PARAMETRIC EQUATIONS CROSSES ITSELF

In this section, we will learn how to find the values of the parameter t, for which the graph of the parametric equations x = f(t) and y = g(t) crosses itself.

Problem 1 :

Find the value of t where the graph of the parametric equations

x = t3 - t + 3

y = t2 - 3

crosses itself.

Solution :

Problem 2 :

Find the value of t where the graph of the parametric equations

x = t3 - 4t

y = t2

crosses itself.

Solution :

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