Question

I want to find a function g(t) such that for any function f(t) the distance from g(t) to both f(t) and f(-t) is the same and forms an equilateral triangle.

Answer 1

Since f is parameterized, it's really more like f(x(t),y(t)). This is just a problem I've made up and there might not necessarily be an answer.

Answer 2

Just came up with it, so I realized if you have:

f(t)=<cos(t), sin(t)> then you're going to have two possible functions for g(t). One is just the center of the circle, the other is outside the circle.

Any thoughts?

Answer 3

Wait. There might be infinite solutions. I don't know now.