HMMT 二月 2000 · CALC 赛 · 第 7 题
HMMT February 2000 — CALC Round — Problem 7
题目详情
英文原题
- 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?
x 02
0 xdy 0
Hint : slop e at a p oin t P on a urv e is j .
Rdx p 2
解析
英文解析
- Using the hin t, tak e . Set this equal to 0 and solv e for x relativ e to x . Plug this indx 0
for x in the giv en family of lines to obtain the en v elop e y = x + ; x > 0 .1
x 0