(1)、x² + y² - 2x - 4y + m = 0
(x² - 2x + 1) + (y² - 4y + 4) - 1 - 4 + m = 0
(x - 1)² + (y - 2)² = 5 - m
5 - m ≥ 0
m ≤ 5
(2)、圆心(1,2)到直线L的距离为
d = |1 + 2 × 2 - 4|/√(1² + 2²) = √5/5
由勾股定理得
(5 - m)² = d² + [(1/2)MN]²
(5 - m)² = 1/5 + (1/4)×(16/5)
(5 - m)² = 1
m = 6(舍弃)
m = 4