# Method to parameterize circles in R3 laying in a plane

## Homework Statement

In general how do i parametrize a circle of radius r at centre (a,b,c) laying on a plane? E.g. (x + y + z = 6)

## The Attempt at a Solution

vela
Staff Emeritus
Homework Helper
You could start with a circle of radius r centered at the origin that lies in the xy-plane. Then apply a rotation so that it lies in the plane parallel to the given plane. Finally, translate it so it's centered at (a,b,c).

LCKurtz
$$R(t) = \langle a,b,c\rangle +r \vec u \cos(t) + r\vec v \sin(t)$$