2.2　圆的一般方程

课后篇巩固探究

A组　基础巩固

1.若圆的方程为(x-1)(x+2)+(y-2)(y+4)=0,则圆心坐标为(　　)

A.(1,-1) B.(1/2 ",-" 1)

C.(-1,2) D.("-" 1/2 ",-" 1)

解析将圆的方程化为(x+1/2)^2+(y+1)2=45/4,

　　即可得到圆心坐标为("-" 1/2 ",-" 1).

答案D

2.将圆x2+y2-2x-4y+1=0平分的直线是(　　)

A.x+y-1=0

B.x+y+3=0

C.x-y+1=0

D.x-y+3=0

解析能将圆平分的直线必过圆心,将圆方程x2+y2-2x-4y+1=0化成标准方程为(x-1)2+(y-2)2=4,知圆心坐标为(1,2),代入四个选项中,只有C符合.故选C.

答案C

3.若关于x,y的方程x2+mxy+y2+2x-y+n=0表示的曲线是圆,则m+n的取值范围是(　　)

A.("-∞," 5/4) B.("-∞," 5/4]

C.(5/4 "," +"∞" ) D.[5/4 "," +"∞" )

解析依题意应有{■(m=0"," @4+1"-" 4n>0"," )┤

　　所以{■(m=0"," @n<5/4 "," )┤于是m+n<5/4.

答案A

4.方程x(x2+y2-4)=0与x2+(x2+y2-4)2=0表示的曲线(　　)

A.都表示一条直线和一个圆

B.前者是两个点,后者是一条直线和一个圆