As shown in the figure, in the rectangular coordinate system, A (- 1, 0) and B (0 0,2), the moving point P moves along the ray BM passing through point B and perpendicular to AB, and the moving speed of point P is 1 unit length per second, and the ray BM intersects with the X axis to find the coordinates of point C, (1) with point P. After t seconds, the triangle with vertices p, q and c is an isosceles triangle. (Point P stops moving when it reaches point C, and point Q also stops moving. ) Find the value of t (4) Under the conditions of (2) and (3), when CQ=CP, find the coordinates of the intersection of the straight line OP and the parabola. The analytic expression of analytic parabola (66 (2)) can be set by three or two formulas, and then the corresponding letter coefficient can be obtained by substituting coordinates; (3) The triangle with vertices P, Q and C is an isosceles triangle, which can be discussed in three cases: CQ=PC, PQ=QC and PQ=PC to construct the equation. The coordinate of point C in the answer (1) is (4,0); (2) Let the analytical formula of parabola passing through points A, B and C be y=ax2+bx+c(a≠0), and substitute the coordinates of points A, B and CQ=t to get the analytical formula of ∴ parabola as y = X2+X+2. (3) Let P and Q. Then PE⊥AC = CQ = BP = T. ∴ There is 2t=BC=, ∴ T =. ② If PQ=QC, as shown in the figure, if Q intersects with point DQ⊥BC and CB intersects with point D, there is CD = PD. From △ABC∽△QDC, we can get PD=CD= T=. (4) When CQ=PC, we can know from (3) that T =, the coordinate of ∴ point P is (2 1), and the analytical formula of ∴ straight line OP is: y=x, so there is x =x2+x+2, namely x2-2x-4.