It is known that the minimum value of the sum of the distances from the moving point P on the parabola y2 = 4x to the lines L1 and L2 is () A. 2B. 3C. 115D. 3716

It is known that the minimum value of the sum of the distances from the moving point P on the parabola y2 = 4x to the lines L1 and L2 is () A. 2B. 3C. 115D. 3716

The straight line L2: x = - 1 is the directrix of the parabola y2 = 4x. According to the definition of the parabola, the distance from P to L2 is equal to the distance from P to the focus f (1,0) of the parabola. Therefore, the problem is to find a point P on the parabola y2 = 4x so that the sum of the distances from P to the point F (1,0) and the straight line L1 is the minimum. The minimum value is the distance from F (1,0) to the straight line L1: 4x-3y + 6 = 0, i.e. d = | 4 − 0 + 6 | 5 = 2, so choose a