Representing A Plane Curve By A Vector Valued Function

Question

I am given the function $x^2+y^2=25$, and I am suppose to write this as a vector valued function.

I have always been awful at these sort of problems, even with parametric equations, which requires the same process. I just don't understand the concept of "just let x=t;" in this particular case, that just doesn't seem to work.

Answer 1

Do parametrization $$ x = 5\cos t \\ y = 5\sin t $$ so your vector valued function is $$ \mathbf r(t) = 5(\cos t\ \hat{\mathbf i}+\sin t \hat{\mathbf j}) $$