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Home / Doubts and Solutions/KERALA/Class 11 Science/Mathematics

Find the locus of the set of points P such that distence from A(2,3,4) is equal to twice the distence from B(-2,1,2).
 
[ I took P as (x,y,z) and found distence from A and distence from B. Now what?]

Asked by Deebu 28th December 2014, 12:23 AM
Answered by Expert
Answer:
L e t space t h e space c o o r d i n a t e s space o f space t h e space p o i n t space P space b e space P left parenthesis x comma y comma z right parenthesis. G i v e n space t h a t space A equals A left parenthesis 2 comma 3 comma 4 right parenthesis space a n d space B equals B left parenthesis minus 2 comma 1 comma 2 right parenthesis. G i v e n space t h a t space A P equals 2 P B rightwards double arrow square root of open parentheses x minus 2 close parentheses squared plus open parentheses y minus 3 close parentheses squared plus open parentheses z minus 4 close parentheses squared end root equals 2 cross times square root of open parentheses x plus 2 close parentheses squared plus open parentheses y minus 1 close parentheses squared plus open parentheses z minus 2 close parentheses squared end root S q u a r i n g space b o t h space t h e space s i d e s comma space w e space h a v e comma A P squared equals 4 P B squared rightwards double arrow open parentheses x minus 2 close parentheses squared plus open parentheses y minus 3 close parentheses squared plus open parentheses z minus 4 close parentheses squared equals 4 open square brackets open parentheses x plus 2 close parentheses squared plus open parentheses y minus 1 close parentheses squared plus open parentheses z minus 2 close parentheses squared close square brackets rightwards double arrow x squared plus 4 minus 4 x plus y squared plus 9 minus 6 y plus z squared plus 16 minus 8 z equals 4 open square brackets x squared plus 4 plus 4 x plus y squared plus 1 minus 2 y plus z squared plus 4 minus 4 z close square brackets rightwards double arrow x squared plus 4 minus 4 x plus y squared plus 9 minus 6 y plus z squared plus 16 minus 8 z equals 4 x squared plus 16 plus 16 x plus 4 y squared plus 4 minus 8 y plus 4 z squared plus 16 minus 16 z rightwards double arrow x squared plus y squared plus z squared minus 4 x minus 6 y minus 8 z plus 29 equals 4 x squared plus 4 y squared plus 4 z squared plus 16 x minus 8 y minus 16 z plus 36 rightwards double arrow 3 x squared plus 3 y squared plus 3 z squared plus 20 x minus 2 y minus 8 z plus 7 equals 0 T h u s space t h e space l o c u s space o f space t h e space s e t space o f space p o i n t s space P space s u c h space t h a t space A P equals 2 P B space i s 3 x squared plus 3 y squared plus 3 z squared plus 20 x minus 2 y minus 8 z plus 7 equals 0
Answered by Expert 28th December 2014, 5:22 PM
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