椭圆知识是高中数学的重点内容,也是高考的必考知识,而直线与椭圆的综合问题又是常考题型,涉及中点、弦长、面积等内容。常规的解题方法是,首先联立直线与椭圆的方程,通过消元转化为一元二次方程,然后结合韦达定理来解答。其优点是学生容易掌握,易操作,但是往往运算量大、烦琐,易出错。而运用“点差法”恰好能解决这一矛盾,特别是在解答与弦的中点有关的问题时,运算简单,结构优美,优势 Ellipse knowledge is the key content of high school mathematics, but also the college entrance examination must be knowledge, and the straight line and the ellipse is a common test questions, involving midpoint, chord, area and so on. The conventional method of solving the problem is to first combine the equations of straight lines and ellipses, and then solve the equations by solving the unidimensional quadratic equation by elimination, and then combine the Vedic theorem. The advantage is that students are easy to grasp, easy to operate, but often computationally expensive, cumbersome and error-prone. The use of “spread method ” just to solve this contradiction, especially in the solution to the mid-point of chord-related problems, the operation is simple, beautiful structure, the advantages