Set two circles c? ，C？ If they are all tangent to the coordinate axis and pass through the point (4, 1), what is the distance between the two centers? c？ What =? What is the approximate image?

Solution: Because the garden is tangent to the two coordinate axes, the distance from the garden center to the two coordinate axes is equal, so the coordinate of the garden center can be set to (m, m);

The circle passes the point (4, 1), so there is the equation m? =(m-4)？ +(m- 1)？ , expand and simplify to get m? - 10m+ 17 = 0； So I have to:

m =( 10√32)/2 = 5 ^ 2√2； Get a c? (5-2√2,5-2√2); c？ (5+2√2,5+2√2);

So, c? c？ √ {2 [(5+2 √ 2)-(5-2 √ 2)]? =√64=8.