从圆X:x2+y2-4x-6y+12=04.从圆C:x2+y2-4x-6y+12=0 外一点P(a,b)向圆作切线PT,T为 切点,且|PT|=|PO|(O为4.从圆C:x2+y2-4x-6y+12=0外一点P(a,b)向圆作切线PT,T为切点,且|PT|=|PO|(O为坐标原点),求|PT|的最小值.及此时点P的
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![从圆X:x2+y2-4x-6y+12=04.从圆C:x2+y2-4x-6y+12=0 外一点P(a,b)向圆作切线PT,T为 切点,且|PT|=|PO|(O为4.从圆C:x2+y2-4x-6y+12=0外一点P(a,b)向圆作切线PT,T为切点,且|PT|=|PO|(O为坐标原点),求|PT|的最小值.及此时点P的](/uploads/image/z/6933149-53-9.jpg?t=%E4%BB%8E%E5%9C%86X%3Ax2%2By2-4x-6y%2B12%3D04.%E4%BB%8E%E5%9C%86C%3Ax2%2By2-4x-6y%2B12%3D0+%E5%A4%96%E4%B8%80%E7%82%B9P%28a%2Cb%29%E5%90%91%E5%9C%86%E4%BD%9C%E5%88%87%E7%BA%BFPT%2CT%E4%B8%BA+%E5%88%87%E7%82%B9%2C%E4%B8%94%7CPT%7C%3D%7CPO%7C%28O%E4%B8%BA4.%E4%BB%8E%E5%9C%86C%3Ax2%2By2-4x-6y%2B12%3D0%E5%A4%96%E4%B8%80%E7%82%B9P%28a%2Cb%29%E5%90%91%E5%9C%86%E4%BD%9C%E5%88%87%E7%BA%BFPT%2CT%E4%B8%BA%E5%88%87%E7%82%B9%2C%E4%B8%94%7CPT%7C%3D%7CPO%7C%28O%E4%B8%BA%E5%9D%90%E6%A0%87%E5%8E%9F%E7%82%B9%29%2C%E6%B1%82%7CPT%7C%E7%9A%84%E6%9C%80%E5%B0%8F%E5%80%BC.%E5%8F%8A%E6%AD%A4%E6%97%B6%E7%82%B9P%E7%9A%84)
从圆X:x2+y2-4x-6y+12=04.从圆C:x2+y2-4x-6y+12=0 外一点P(a,b)向圆作切线PT,T为 切点,且|PT|=|PO|(O为4.从圆C:x2+y2-4x-6y+12=0外一点P(a,b)向圆作切线PT,T为切点,且|PT|=|PO|(O为坐标原点),求|PT|的最小值.及此时点P的
从圆X:x2+y2-4x-6y+12=04.从圆C:x2+y2-4x-6y+12=0 外一点P(a,b)向圆作切线PT,T为 切点,且|PT|=|PO|(O为
4.从圆C:x2+y2-4x-6y+12=0
外一点P(a,b)向圆作切线PT,T为
切点,且|PT|=|PO|(O为坐标原点),
求|PT|的最小值.及此时点P的坐标
从圆X:x2+y2-4x-6y+12=04.从圆C:x2+y2-4x-6y+12=0 外一点P(a,b)向圆作切线PT,T为 切点,且|PT|=|PO|(O为4.从圆C:x2+y2-4x-6y+12=0外一点P(a,b)向圆作切线PT,T为切点,且|PT|=|PO|(O为坐标原点),求|PT|的最小值.及此时点P的
圆的方程:
(x-2)^2+(y-3)^2=1
所以是在(2,3)为圆心,1为直径的圆
过P作PT,所以PT=√(|PC|^2-R^2)=√((a-2)^2+(b-3)^2-1)=PO=√(a^2+b^2)
-->a^2+b^2-4a-6b+12=a^2+b^2
-->4a+6b=12 -->2a+3b=6
求PO最小值则为a^2+b^2最小值
根据柯西不等式得
(a^2+b^2)(4+9)>=(2a+3b)^2
-->a^2+b^2>=36/13
-->PT>=√(36/13)=6√13/13
当且仅当a:b=2:3 即a=12/13 b=18/13 时成立