已知点P(x,y)是圆x^2+y^2-6x-4y+12=0上一点,求:.已知点P(x,y)是圆x^2+y^2-6x-4y+12=0上一点,求:(1) x^2+y^2的最值.(2) x+y的最值.(3) P到直线x+y-1=0的距离d的最值.
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![已知点P(x,y)是圆x^2+y^2-6x-4y+12=0上一点,求:.已知点P(x,y)是圆x^2+y^2-6x-4y+12=0上一点,求:(1) x^2+y^2的最值.(2) x+y的最值.(3) P到直线x+y-1=0的距离d的最值.](/uploads/image/z/2102788-28-8.jpg?t=%E5%B7%B2%E7%9F%A5%E7%82%B9P%28x%2Cy%29%E6%98%AF%E5%9C%86x%5E2%2By%5E2-6x-4y%2B12%3D0%E4%B8%8A%E4%B8%80%E7%82%B9%2C%E6%B1%82%EF%BC%9A.%E5%B7%B2%E7%9F%A5%E7%82%B9P%28x%2Cy%29%E6%98%AF%E5%9C%86x%5E2%2By%5E2-6x-4y%2B12%3D0%E4%B8%8A%E4%B8%80%E7%82%B9%2C%E6%B1%82%EF%BC%9A%281%29+x%5E2%2By%5E2%E7%9A%84%E6%9C%80%E5%80%BC.%282%29+x%2By%E7%9A%84%E6%9C%80%E5%80%BC.%283%29+P%E5%88%B0%E7%9B%B4%E7%BA%BFx%2By-1%3D0%E7%9A%84%E8%B7%9D%E7%A6%BBd%E7%9A%84%E6%9C%80%E5%80%BC.)
已知点P(x,y)是圆x^2+y^2-6x-4y+12=0上一点,求:.已知点P(x,y)是圆x^2+y^2-6x-4y+12=0上一点,求:(1) x^2+y^2的最值.(2) x+y的最值.(3) P到直线x+y-1=0的距离d的最值.
已知点P(x,y)是圆x^2+y^2-6x-4y+12=0上一点,求:.
已知点P(x,y)是圆x^2+y^2-6x-4y+12=0上一点,求:
(1) x^2+y^2的最值.
(2) x+y的最值.
(3) P到直线x+y-1=0的距离d的最值.
已知点P(x,y)是圆x^2+y^2-6x-4y+12=0上一点,求:.已知点P(x,y)是圆x^2+y^2-6x-4y+12=0上一点,求:(1) x^2+y^2的最值.(2) x+y的最值.(3) P到直线x+y-1=0的距离d的最值.
圆1:(x-3)^2+(y-2)^2=1,圆心(3,2),半径r=1
(1) 圆2:R^2=x^2+y^2,
两圆内切时,R最大,两圆外切时R最小
圆心距d1=√(3^2+2^2)=√(13),
max(R^2)=(d2+r)2=[√(13)+1]2=14+2√(13)
min(R^2)=(d2-r)2=[√(13)-1]2=14-2√(13)
(2) b=x+y,y=-x+b,与圆相切时b取得最值
d2=|3+2-b|/√2=r=1,5-b=±√2,b=5±√2
max(b)=5+√2,min(b)=5-√2
(3) 圆心(3,2)到直线x+y-1=0的距离为d3,
则P到直线x+y-1=0的距离d的最大值为d3+r,最小值为d3-r
d3=|3+2-1|/√2=2√2,
max(d)=d3+r=2√2+1,min(d)=d3-r=2√2-1