This topic mainly examines the standard equation of parabola, the application of the positional relationship between straight line and conic curve, the application of Vieta theorem and chord length formula, which embodies the mathematical idea of classified discussion. The answer is/exercise/math /804088. In fact, this problem is also a mid-range problem, which is not too difficult.

It is known that the focus of parabola C is: y 2 = 2px (p > 0) is F, the intersection of straight line y=4 and Y axis is P, the intersection of straight line y = 4 and C is Q, and | qf | = 5/4 | pq |.

(a) to find the equation of c;

(2) The straight line L passing through F intersects at point A and point B. If the perpendicular line L' of AB intersects at point M and point N, and A, M, B and N are on the same circle, find the equation of L. 。