HMMT 二月 2004 · 冲刺赛 · 第 7 题

英文解析

7. Find the shortest distance from the line 3 x + 4 y = 25 to the circle x + y = 6 x − 8 y .
   Solution: 7 / 5
   2 2 2
   The circle is ( x − 3) + ( y + 4) = 5 . The center (3 , − 4) is a distance of
   | 3 · 3 + 4 · − 4 − 25 | 32
   √ =
   2 2
   3 + 45
   from the line, so we subtract 5 for the radius of the circle and get 7 / 5.