Question

If you are given a parametric equation and a function, how would you find which point they meet/cross each other?

Answer 1

By "parametric equation", I assume that you mean a parametric point:

`(x(t), y(t))`

And I assume that you are given a function:

`y = f(x)`

The point of intersection can be found by writing the equation:

`y(t) = f(x(t))`

This will give you an equation that contains only the variable t.

Solve the equation for the value (or values) of t and the evaluate the parametric point at that value (or values); this will give you the point (or points) of intersection.