若圆(x-1)²+(y+1)²=4与y=x+b相切,则实数b的值等于答案是-2+2根号2或-2-2根号2问下这题的具体解题步骤
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![若圆(x-1)²+(y+1)²=4与y=x+b相切,则实数b的值等于答案是-2+2根号2或-2-2根号2问下这题的具体解题步骤](/uploads/image/z/14681784-48-4.jpg?t=%E8%8B%A5%E5%9C%86%28x-1%29%26%23178%3B%2B%28y%2B1%29%26%23178%3B%3D4%E4%B8%8Ey%3Dx%2Bb%E7%9B%B8%E5%88%87%2C%E5%88%99%E5%AE%9E%E6%95%B0b%E7%9A%84%E5%80%BC%E7%AD%89%E4%BA%8E%E7%AD%94%E6%A1%88%E6%98%AF-2%2B2%E6%A0%B9%E5%8F%B72%E6%88%96-2-2%E6%A0%B9%E5%8F%B72%E9%97%AE%E4%B8%8B%E8%BF%99%E9%A2%98%E7%9A%84%E5%85%B7%E4%BD%93%E8%A7%A3%E9%A2%98%E6%AD%A5%E9%AA%A4)
若圆(x-1)²+(y+1)²=4与y=x+b相切,则实数b的值等于答案是-2+2根号2或-2-2根号2问下这题的具体解题步骤
若圆(x-1)²+(y+1)²=4与y=x+b相切,则实数b的值等于
答案是-2+2根号2或-2-2根号2
问下这题的具体解题步骤
若圆(x-1)²+(y+1)²=4与y=x+b相切,则实数b的值等于答案是-2+2根号2或-2-2根号2问下这题的具体解题步骤
答:
圆与直线相切,表示圆心到直线的距离d=圆半径R
圆(x-1)²+(y+1)²=4=2²,圆心(1,-1),半径R=2
直线y=x+b,x-y+b=0
所以:
d=|1+1+b|/√(1²+1²)=2
|b+2|=2√2
解得:b=-2+2√2或者b=-2-2√2
直线与圆相切,即圆心到直线的距离d=半径r
半径r=2
圆心(1,-1)
直线:x-y+b=0
距离d=|1-(-1)+b|/√(1²+1²)
=|2+b|/√2
|2+b|/√2=2
b=-2±2√2