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江苏省新课标高中数学限时训练4 苏教版必修2

第4练

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1、方程 x 2 ? y 2 ? 4x ? 2 y ? 5m ? 0 表示圆的条件是__________________.

2、 M (3,0) 是圆 x 2 ? y 2 ? 8x ? 2 y ? 10 ? 0 内一点,过 M 点最长的弦所在的直线 方程是____ ___.

3、设圆 x 2 ? y 2 ? 4x ? 5 ? 0 的弦 AB 的中点为 P(3,1),则直线 AB 的方程是

.

4、经过点 M (2,?1) 作圆 x 2 ? y 2 ? 5 的切线,则切线的方程为___

__.

5、平行于直线 2 x ? y ? 1 ? 0 且与圆 x 2 ? y 2 ? 5 相切的直线的方程是 ___ __.

6、已知圆 C : ( x ? 1) ? ( y ? 2) ? 4 及直线 l:x-y+3=0,则直线 l 被圆 C 截得的
2 2

弦长为_____

_____.

2 2 2 2 7、若实数 x、y 满足 x ? y ? 4x ? 2 y ? 4 ? 0 ,则 x ? y 的最大值是__

_.

2 2 2 2 2 8、 集合 A ? ? x, y ? x ? y ? 4 , B ? ? x, y ? ( x ? 3) ? ( y ? 4) ? r , 其中 r>0, 若 A? B 中

?

?

?

?

有且仅有一个元素,则 r 的值是___________.
2 2 9、一直线过点 P ( ?3,? ) ,被圆 x ? y ? 25 截得的弦长为 8,

3 2

求此弦所在的直线方程.

10、若直线 4 x ? 3 y ? a ? 0与圆x 2 ? y 2 ? 100。 (1)相交; (2)相切; (3)相离;分别求实 属 a 的取值范围.


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