That is (x- 1)? +(y-2)？ =5 meters

When 5-m > 0, it meets the meaning of the question, that is, m < 5.

2. Let the coordinates of two points where a circle intersects a straight line be M(x 1, y 1)N(x2, y2) respectively.

∫x+2y-4 = 0∴x=4-2y②

Bring ② into ① and simplify it to: 5y? - 16y+8+m=0

∴y 1 y2 =(8+m)/5③y 1+y2 = 16/5

x 1 x2 =(4-2y 1)(4-2y 2)= 16-8y 1-8y 2+4y 1 y2

? = 16-8(y 1+y2)+4y 1 y2

? =-8/5 + 4m/5？ ④

x 1+x2 = 8-2(y 1+y2)= 8-32/5 = 8/5

So MN= root number (1+k 2) | x2-x 1 | = root number (1+4) (64/25-4 (-8/5+4m/5)) = root number 5* root number (66).

That is, the root number (224/25- 16m/5)=4/5.

224/25- 16m/5= 16/25

The solution is m= 13/5.