2) According to the meaning of the question, we can set the analytical formula of parabola as y=a(x- 1)(x-6) and substitute it into point C to get a= 1/2.

Therefore, y = 1/2 x 2-7/2 x+3.

Substituting the coordinates of point B for verification shows that B is on a parabola.

3) According to the meaning of the question, in the quadrilateral BCPQ, the side length of BC is fixed. If the perimeter is the smallest, the minimum value of | BQ |+PQ |+PC | should be taken. From the shortest line segment between two points, we can take the symmetry point B'(-2, -2) of point B and the symmetry point C'(5, 2) of point C about the X axis to connect B'.

The straight line where B'C' lies is y = 4/7 x -6/7, p (3/2,0) and q (0 0,6/7).

The minimum circumference is 3+√ 65;