1.已知圆C:(x-3)^2+(y-4)^2=4及两点A(-1,0)与B(1,0).p(x,y)为圆c上任意一点,求|AP|^2+|BP|^2的最小值.2.已知点A是圆C:(x-a)^2+(y+2)^2=a^2+10上任一点,且点A关于直线l:x+2y+1=0的对称点也在圆上,求实数a的值.SO
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![1.已知圆C:(x-3)^2+(y-4)^2=4及两点A(-1,0)与B(1,0).p(x,y)为圆c上任意一点,求|AP|^2+|BP|^2的最小值.2.已知点A是圆C:(x-a)^2+(y+2)^2=a^2+10上任一点,且点A关于直线l:x+2y+1=0的对称点也在圆上,求实数a的值.SO](/uploads/image/z/4514438-38-8.jpg?t=1.%E5%B7%B2%E7%9F%A5%E5%9C%86C%EF%BC%9A%EF%BC%88x-3%29%5E2%2B%28y-4%29%5E2%3D4%E5%8F%8A%E4%B8%A4%E7%82%B9A%28-1%2C0%29%E4%B8%8EB%281%2C0%29.p%28x%2Cy%29%E4%B8%BA%E5%9C%86c%E4%B8%8A%E4%BB%BB%E6%84%8F%E4%B8%80%E7%82%B9%2C%E6%B1%82%7CAP%7C%5E2%2B%7CBP%7C%5E2%E7%9A%84%E6%9C%80%E5%B0%8F%E5%80%BC.2.%E5%B7%B2%E7%9F%A5%E7%82%B9A%E6%98%AF%E5%9C%86C%EF%BC%9A%EF%BC%88x-a%29%5E2%2B%28y%2B2%29%5E2%3Da%5E2%2B10%E4%B8%8A%E4%BB%BB%E4%B8%80%E7%82%B9%2C%E4%B8%94%E7%82%B9A%E5%85%B3%E4%BA%8E%E7%9B%B4%E7%BA%BFl%3Ax%2B2y%2B1%3D0%E7%9A%84%E5%AF%B9%E7%A7%B0%E7%82%B9%E4%B9%9F%E5%9C%A8%E5%9C%86%E4%B8%8A%2C%E6%B1%82%E5%AE%9E%E6%95%B0a%E7%9A%84%E5%80%BC.SO)
1.已知圆C:(x-3)^2+(y-4)^2=4及两点A(-1,0)与B(1,0).p(x,y)为圆c上任意一点,求|AP|^2+|BP|^2的最小值.2.已知点A是圆C:(x-a)^2+(y+2)^2=a^2+10上任一点,且点A关于直线l:x+2y+1=0的对称点也在圆上,求实数a的值.SO
1.已知圆C:(x-3)^2+(y-4)^2=4及两点A(-1,0)与B(1,0).p(x,y)为圆c上任意一点,求|AP|^2+|BP|^2的最小值.
2.已知点A是圆C:(x-a)^2+(y+2)^2=a^2+10上任一点,且点A关于直线l:x+2y+1=0的对称点也在圆上,求实数a的值.
SOS!明天要交的!
1.已知圆C:(x-3)^2+(y-4)^2=4及两点A(-1,0)与B(1,0).p(x,y)为圆c上任意一点,求|AP|^2+|BP|^2的最小值.2.已知点A是圆C:(x-a)^2+(y+2)^2=a^2+10上任一点,且点A关于直线l:x+2y+1=0的对称点也在圆上,求实数a的值.SO
1、设P(3+2cost,4+2sint)
|AP|^2=36+16(sint+cost)
|BP|^2=24+16sint+8cost
|AP|^2+|BP|^2=60+32sint+24cost
=60+40(sint*(4/5)+cost*(3/5))
=60+40sin(t+a)
其中 cosa=4/5
最小值=60-40=20
2、点A关于直线l:x+2y+1=0的对称点也在圆上
则圆的圆心在直线l上
圆心(a,-2)
a-4+1=0
a=3