I have a question as follows:
Determine whether the following trajectory lies on a circle. If so, find the radius of the circle and show that the position vector and velocity vector are everywhere orthogonal.
$r(t)=\langle2\sin(t)+\sqrt{21}\cos(t),\ \ \sqrt{21}\sin(t)-2\cos(t)\rangle$ for $0 \le t \le2\pi$
I'm not really sure where to start with this one. I found the velocity vector to be
$r'(t)=\langle2\cos(t)-\sqrt{21}\sin(t),\ \ \sqrt{21}\cos(t)+2\sin(t)\rangle$
but I'm not sure how to determine if it's on a circle, or the rest of the question…
Best Answer
It does because $x^2(t) + y^2(t) = 25 = 5^2 \Rightarrow r = 5, C = (0,0)$