HMMT 二月 2000 · CALC 赛 · 第 7 题
HMMT February 2000 — CALC Round — Problem 7
题目详情
- An en v elop e of a set of lines is a urv e tangen t to all of them. What is the en v elop e of 2 1 the family of lines y = + x (1 ), with x ranging o v er the p ositiv e real n um b ers? 2 0 x x 0 0 dy Hint : slop e at a p oin t P on a urv e is j . P dx R 2
解析
- Using the hin t, tak e . Set this equal to 0 and solv e for x relativ e to x . Plug this in 0 dx 1 for x in the giv en family of lines to obtain the en v elop e y = x + ; x > 0 . 0 x