It is known that the parabolic equation y2 = 4x, the line L passing through the fixed point P (- 2,1) and the slope k intersect the parabolic equation y2 = 4x at two different points. The range of the slope k is obtained

It is known that the parabolic equation y2 = 4x, the line L passing through the fixed point P (- 2,1) and the slope k intersect the parabolic equation y2 = 4x at two different points. The range of the slope k is obtained

The equation of line L is: Y-1 = K (x + 2), which is changed into y = KX + 2K + 1. Simultaneous y = KX + 2K + 1Y2 = 4x, which is changed into k2x2 + (2k + 4k2-4) x + (2k + 1) 2 = 0. The line L and parabola y2 = 4x intersect at two different points. The solution is - 1 < K < 12, and K ≠ 0. The range of slope k is - 1 < K < 12, and K ≠ 0