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高中数学圆的标准方程课件5 新课标 人教版 必修2(B).ppt_图文

圆的标准方程
教学目标:掌握圆的标准方程 会求圆的标准方程并能简单应用

教学难点:求圆的标准方程和 圆的标准方程的应用

一、问题:圆的定义是什么? 平面内到一个定点的距离相等的点的集合. 二、确定圆的条件又是什么?

定点 和 定距离
圆心O 半径 r

圆的标准方程的推导
已知圆心为O(a,b),半径为 r ,求圆的方程.

分 析 : 设 圆 上 的 任 意个 一 点P( x , y ) 由 于 PO= ( x ? a ) ? ( y ? b ) ? r
2 2

两边平方得 : ( x ? a ) ? ( y ? b) =r
2 2

2

圆的标准方程 特别地:圆心为(0,0)时,x2+y2=r2

练1:以C(4,-6)为圆心、半径为3的圆的 2+(y+6)2=9 (x-4) 方程是____________; 练2:经过点P(5,1),圆心为C(6,-2)的圆的 2+(y+2)2=10 (x-6) 方程是___________; (0,0) 练3:方程x2+y2=0表示什么图形______ 练4:方程(x-1)2=9-(y+3)2表示什么图形 圆心是(1,-3)半径是3的圆 _____________________; 练5:方程y= 4 ? x 2 表示什么图形 圆心在原点,半径为2的上半圆

例1:已知两点M(4,9),N(6,3),求以MN为直 径的圆的方程 分析:先用中点坐标公式求得圆心(5,6), 再用距离公式求得半径r2=10

(x-5)2 +(y-6)2=10

例2:圆过点P(2,-1),与直线x-y=1相切,圆 心在直线y=-2x上,求这个圆的方程 分析:(待定系数法)

练6:圆(x+1)2+(y-3)2=16关于x轴对称的 2+(y+3)2=16 (x+1) 圆方程是___________

关于直线x+y=0对称的圆的方程是 _____________ (x+3)2+(y-1)2=16

作业:课本P103 A1、 P104 B2;

《同步》P62 右7


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