2022年圆与方程知识点总结汇编 .pdf
学习-好资料更多精品文档圆梦教育中心圆与方程知识点总结1.圆的标准方程：以点),(baC为圆心，r 为半径的圆的标准方程是222)()(rbyax.特例：圆心在坐标原点，半径为r 的圆的方程是：222ryx.2.点与圆的位置关系：(1).设点到圆心的距离为d，圆半径为r：a.点在圆内dr；b.点在圆上d=r；c.点在圆外dr (2).给定点),(00yxM及圆222)()(:rbyaxC.M 在圆 C 内22020)()(rbyax M 在圆 C 上22020)()rbyax（M 在圆 C 外22020)()(rbyax（3）涉及最值：圆外一点B，圆上一动点P，讨论PB的最值minPBBNBCrmaxPBBMBCr圆内一点A，圆上一动点P，讨论PA的最值minPAANrACmaxPAAMrAC思考：过此A点作最短的弦？（此弦垂直AC）3.圆的一般方程：022FEyDxyx.(1)当0422FED时，方程表示一个圆，其中圆心2,2EDC，半径2422FEDr.(2)当0422FED时，方程表示一个点2,2ED.(3)当0422FED时，方程不表示任何图形.学习-好资料更多精品文档注：方程022FEyDxCyBxyAx表示圆的充要条件是：0B且0CA且0422AFED.4.直线与圆的位置关系：直线0CByAx与圆222)()(rbyax圆心到直线的距离22BACBbAad1）无交点直线与圆相离rd；2）只有一个交点直线与圆相切rd；3）有两个交点直线与圆相交rd；弦长|AB|=222drdrd=rrd还可以利用直线方程与圆的方程联立方程组0022FEyDxyxCByAx求解，通过解的个数来判断：（1）当0时，直线与圆有2 个交点，直线与圆相交；（2）当0时，直线与圆只有1 个交点，直线与圆相切；（3）当0时，直线与圆没有交点，直线与圆相离；5.两圆的位置关系（1）设两圆2121211)()(:rbyaxC与圆2222222)()(:rbyaxC，圆心距221221)()(bbaad条公切线外离421rrd；条公切线外切321rrd；条公切线相交22121rrdrr；条公切线内切121rrd；无公切线内含210rrd；外离外切相交内切（2）两圆公共弦所在直线方程文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8学习-好资料更多精品文档圆1C：221110 xyD xE yF，圆2C：222220 xyD xE yF，则1212120DDxEEyFF为两相交圆公共弦方程.补充说明：若1C与2C相切，则表示其中一条公切线方程；若1C与2C相离，则表示连心线的中垂线方程.（3）圆系问题过 两 圆1C：221110 xyD xE yF和2C：222220 xyD xE yF交 点 的 圆 系 方 程 为22221112220 xyD xE yFxyD xE yF（1）补充：上述圆系不包括2C；2）当1时，表示过两圆交点的直线方程（公共弦）过直线0AxByC与圆220 xyDxEyF交点的圆系方程为220 xyDxEyFAxByC6.过一点作圆的切线的方程：(1)过圆外一点的切线：k 不存在，验证是否成立k 存在，设点斜式方程，用圆心到该直线距离=半径，即1)()(2110101RxakybRxxkyy求解 k，得到切线方程【一定两解】例 1.经过点 P(1，2)点作圆(x+1)2+(y2)2=4 的切线，则切线方程为。(2)过圆上一点的切线方程：圆(xa)2+(yb)2=r2，圆上一点为(x0，y0)，则过此点的切线方程为(x0a)(xa)+(y0b)(yb)=r2文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8学习-好资料更多精品文档特别地，过圆222ryx上一点),(00yxP的切线方程为200ryyxx.例 2.经过点 P(4，8)点作圆(x+7)2+(y+8)2=9 的切线，则切线方程为。7切点弦(1)过C：222)()(rbyax外一点),(00yxP作C的两条切线，切点分别为BA、，则切点弦AB所在直线方程为：200)()(rbybyaxax8.切线长：若圆的方程为(x a)2(y b)2=r2，则过圆外一点P(x0,y0)的切线长为d=22020b)(+)(ryax9.圆心的三个重要几何性质：圆心在过切点且与切线垂直的直线上；圆心在某一条弦的中垂线上；两圆内切或外切时，切点与两圆圆心三点共线。10.两个圆相交的公共弦长及公共弦所在的直线方程的求法例.已知圆 C1：x2+y2 2x=0 和圆 C2：x2+y2+4 y=0，试判断圆和位置关系，若相交，则设其交点为A、B，试求出它们的公共弦AB的方程及公共弦长。文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8文档编码:CP6O3V5I4D8 HB7K8C3W5H10 ZT5O8B8G4N8
