如图,已知圆C:(x-1)²+(y-2)²=2,点P(2,-1).过P点做圆C的切线PA,PB,A,B为切点.(1)求切线PA,PB的方程;(2)求切线长PA
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![如图,已知圆C:(x-1)²+(y-2)²=2,点P(2,-1).过P点做圆C的切线PA,PB,A,B为切点.(1)求切线PA,PB的方程;(2)求切线长PA](/uploads/image/z/5261318-62-8.jpg?t=%E5%A6%82%E5%9B%BE%2C%E5%B7%B2%E7%9F%A5%E5%9C%86C%3A%EF%BC%88x%EF%BC%8D1%EF%BC%89%26%23178%3B%2B%EF%BC%88y%EF%BC%8D2%EF%BC%89%26%23178%3B%EF%BC%9D2%2C%E7%82%B9P%282%2C-1%29.%E8%BF%87P%E7%82%B9%E5%81%9A%E5%9C%86C%E7%9A%84%E5%88%87%E7%BA%BFPA%2CPB%2CA%2CB%E4%B8%BA%E5%88%87%E7%82%B9.%EF%BC%881%EF%BC%89%E6%B1%82%E5%88%87%E7%BA%BFPA%2CPB%E7%9A%84%E6%96%B9%E7%A8%8B%EF%BC%9B%EF%BC%882%EF%BC%89%E6%B1%82%E5%88%87%E7%BA%BF%E9%95%BFPA)
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如图,已知圆C:(x-1)²+(y-2)²=2,点P(2,-1).过P点做圆C的切线PA,PB,A,B为切点.(1)求切线PA,PB的方程;(2)求切线长PA
如图,已知圆C:(x-1)²+(y-2)²=2,点P(2,-1).过P点做圆C的切线PA,PB,A,B为切点.(1)求切线PA,PB的方程;(2)求切线长PA
如图,已知圆C:(x-1)²+(y-2)²=2,点P(2,-1).过P点做圆C的切线PA,PB,A,B为切点.(1)求切线PA,PB的方程;(2)求切线长PA
解:
(1)过P点的圆的切线为
y+1=k(x-2)
--->kx-y-2k-1=0
它与圆心(1,2)的距离等于半径 "根2",故
|k-2-2k-1|/根(1+k^2)=根2
--->k^2-6k-7=0
解得,k=7,或k=-1.
故PA、PB分别为
x+y-1=0
7x-y-15=0
(2)在直角三角形PAC中,由两点距公式易得,|PC|=根10
故|PA|^2=|PB|^2=|PC|^2-|AC|^2=10-2=8
即过P点的圆的切线PA长是: 2根2.