Let f(x) and g(x) be denoting some plane curves in the x-y plane. Now, suppose I want to find intersection of f(x) and g(x). This is precisely the point where distance between curves is minimized. Or even better, the square of the distance
Consider,
$ D= (x_1 -x_2)^2 + (y_1 - y_2)^2$
where$ x_1 $and $x_2$ are the points the curves when they intersect, now this becomes
$ D= (x_1 - x_2 )^2 + (f(x_1) - g(x_2))^2$
Now, problem is this leads me to $x_1 = x_2$ and $f(x_1) = g(x_2)$
Which is indeed the criteria of intersecction, but would it be possible to find exact points where they intersect using this?