A Basic Differential Geometry Question

[iceblits]

Suppose x(t) is a curve in ℝ^2 satisfying x*x'=0 where * is the dot product. Show that x(t) is a circle.

The hint says find the derivative of ||x(t)||^2 which is zero and doesn't tell me much.

I was hoping for x*x= r, r a constant.

 

[micromass]

If the derivative of a function is constant zero. What can you tell about the original function?

 

[iceblits]

Oh my gosh I can't believe I even posted this question haha!..its a constant of course