题目内容
如图,⊙P的圆心为P(-3,2),半径为3,直线MN过点M(5,0)且平行于y轴,点N在点M的上方,(1)在图中作出⊙P关于y轴对称的⊙P′,根据作图直接写出⊙P′与直线MN的位置关系.
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(2)若点N在(1)中的⊙P′上,求PN的长.
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(2)若点N在(1)中的⊙P′上,求PN的长.
(1)见解析 (2)
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分析:在平面直角坐标系中,易知点P′的坐标为(3,2),⊙P′的半径和⊙P的半径相等为3,这样⊙P′就被确定,因为点N在直线MN上,直线MN过(5,0)点且平行于y轴,直线PP′⊥MN,这样利用勾股定理就可求得PN的长度.
解:(1)如图,⊙P′的圆心为(3,2),半径为3,与直线MN相交.
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(2)连接PP′,交直线MN于点A,
∵点P、P′的纵坐标相同,∴PP′∥x轴,
又∵MN∥y轴,∴PP′⊥MN,
∴点A的坐标为(5,2).
在Rt△P′NA中,P′N=3,P′A=5-3=2.
∴AN=
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在Rt△PAN中,PA=5-(-3)=8,AN=
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∴PN=
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