The Cayley–Bacharach theorem is also used to prove that the group operation on cubic elliptic curves is associative. The same group operation can be applied on a cone if we choose a point on the cone and a line in the plane. The sum of and is obtained by first finding the intersection point of line with , which is . Next and add up to the second intersection point of the cone with line , which is . Thus if is the second intersection point of the cone with line , then