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2013年高考陕西理科数学第20题是:已知动圆过定点A(4,0),且在y轴上截得弦MN的长为8.(Ⅰ)求动圆圆心的轨迹C的方程;(Ⅱ)已知点B(-1,0),设不垂直于x轴的直线L与轨迹C交于不同的两点P,Q,若x轴是∠PBQ的角平分线,证明直线L过定点.推广已知抛物线C:y2=2px(p为正常数),点A(-p4,0),设不垂直于x轴的直线L与抛物线C交于不同的两点M,N,若x轴是∠MAN的角平分线,求证:直线L恒过定点(p4,0).证明由题意,设直线L的方程为y=kx
2013 college entrance examination in Shaanxi Science 20 is: known to move around the fixed point A (4,0), and in the y-axis truncated string MN is 8. (Ⅰ) Find the trajectory of the center of the circle C equation ; (II) Known point B (-1, 0), set the line L and the track C not perpendicular to the x axis to intersect at different two points P and Q. If the x axis is the angle bisector of ∠PBQ, prove that the straight line L over a fixed point to promote the known parabola C: y2 = 2px (p is a normal number), point A (-p4,0), set not perpendicular to the x-axis of the line L and parabola C at different points M, N , If the x-axis is the angle bisector of ∠MAN, verify that the straight line L is constant over a point (p4,0). Proof of the problem, the equation for a straight line L is y = kx