If A (-2,2,3) and B(13,-3,13) are two points such that 3PA = 2PB, find the locus of P.

Asked by Topperlearning User | 13th Nov, 2016, 09:44: PM

Expert Answer:

L e t space P equals left parenthesis x comma y comma z right parenthesis
G i v e n space 3 P A equals 2 P B
rightwards double arrow 9 P A squared equals 4 P B squared
rightwards double arrow 9 left square bracket left parenthesis x plus 2 right parenthesis squared plus left parenthesis y minus 2 right parenthesis squared plus left parenthesis z minus 3 right parenthesis squared right square bracket equals 4 left square bracket left parenthesis x minus 13 right parenthesis squared plus left parenthesis y plus 3 right parenthesis squared plus left parenthesis z minus 13 right parenthesis squared right square bracket
rightwards double arrow 9 left square bracket x squared plus y squared plus z squared plus 4 x minus 4 y minus 6 z plus 17 right square bracket equals 4 left square bracket x squared plus y squared plus z squared minus 26 x plus 6 y minus 26 z plus 347 right square bracket
rightwards double arrow 5 x squared plus 5 y squared plus 5 z squared plus 140 x minus 60 y plus 50 z minus 1235 equals 0
rightwards double arrow x squared plus y squared plus z squared plus 28 x minus 12 y plus 10 z minus 247 equals 0

Answered by  | 13th Nov, 2016, 11:44: PM