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85年湖北省六市的高考预选题的第八题为: 长度为a的线段AB两端点在抛物线x~2=2py (a≥2p≥0)上运动,以AB的中点C为圆心作圆和抛物线的准线相切,求圆C的最小半径。对上述问题进行追溯和引伸,我们可以发现这是一个很有内涵的问题,解出这一道题目,可以使我们明白一类问题。一、关于解法的思考解数学题,通常是通过联想寻找解题的方法,首先是寻觅问题的原有模型,并在旧问题的解法中形成解决新问题的方法。因此探求解决这个问题,会使我们联想起一个熟知的问题,即:“以抛物线焦点弦为直径的圆与抛物
The eighth question of the college entrance examination pre-selection questions in the six cities of Hubei Province in the year of 85 is: The line AB at the length a is on the parabola x~2=2py (a≥2p≥0), and the center point AB is the center point of AB. The quasi-line of the circle and the parabola is tangent. Find the minimum radius of the circle C. After retrospective and extension of the above problems, we can find that this is a very connotative problem. Solving this problem can make us understand a class of problems. First, the solution to solving problems Math problems, usually through the association to find ways to solve problems, the first is to find the original model of the problem, and in the solution of the old problem to form a solution to new problems. So searching for a solution to this problem will remind us of a well-known problem: "Circles and parabolas with a diameter of a parabola focus chord.