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一、两条曲线间的位置关系(一) 直线与二次曲线的位置关系例1 已知实数A、B、C满足A~2+V~2=2C~2≠0,求证直线Ax+By+C=0与圆x~2+y~2=1交于不同的两点P,Q,并求弦P的的长。分析:证明的一般思路是:列方程组,消元,证明△>0,这是对于证明一般二次曲线与直线相交的通用方法.对于圆,还有其特殊的几何方法:证明圆心到直线的距离小于圆半径。
Positional relationship between one or two curves (1) Positional relationship between straight line and quadratic curve Example 1 It is known that real numbers A, B, and C satisfy A~2+V~2=2C~2≠0, and the verification line Ax+By +C=0 intersects with the circle x~2+y~2=1 at two different points P,Q, and finds the length of the string P. Analysis: The general idea of the proof is: list equations, elimination, prove △> 0, this is a general method to prove the intersection of the general quadratic curve and the straight line. For the circle, there is also a special geometric method: prove the center of the circle to the straight line The distance is less than the circle radius.