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HMMT 二月 2004 · 冲刺赛 · 第 7 题

HMMT February 2004 — Guts Round — Problem 7

专题
Discrete Math / 离散数学
难度
L3
来源
HMMT

题目详情

  1. [6] Find the shortest distance from the line 3 x +4 y = 25 to the circle x + y = 6 x − 8 y .
解析
  1. 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 5 3 + 4 from the line, so we subtract 5 for the radius of the circle and get 7 / 5.