推 nokol :感謝您... 05/23 14:07
※ 引述《nokol (無賴)》之銘言:
: 拋物線y^2=12x上求一點P,使得P到焦點F與定點A(5,4)之距離和
: PF+PA為最小,求P的座標為何???
: 想了很久,沒啥頭緒,總覺得跟拋物線的定義有關...
: 煩請站上各位大師指點一下了,感謝...
optical property
1. light will go the shortest distance.
2. a light emitted fromthe focus will reflect as a parallel light.
F(3,0)
a parallel line through (5,4) is y=4
hence 16=12x, x=4/3
then min PF+PA=√[(4/3 - 3)^2 + 4^2] + |5-4/3|
=√(25+144) / 3 + 11/3
=8
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※ 編輯: JohnMash 來自: 27.147.57.77 (05/23 13:54)