The linear equation which passes through the fixed point P (0,1) and has only one common point with the parabola y2 = 2x is______ ．

The linear equation which passes through the fixed point P (0,1) and has only one common point with the parabola y2 = 2x is______ ．

① Let the slope of line l be equal to K, then when k = 0, the equation of line L is y = 1, satisfying that there is only one common point between line and parabola y2 = 2x. When k ≠ 0, line L is the tangent of parabola. Let the equation of line l be y = KX + 1, substituting into the equation of parabola, we can get k2x2 + (2k-2) x + 1 = 0, according to the discriminant equal to 0, we can get k = 12, so the tangent equation is & nbsp; (2) when the slope does not exist, the linear equation is x = 0. The test shows that the straight line is tangent to the parabola y2 = 2x. So the answer is: y = 1, or x = 0, or x-2y + 2 = 0