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| 1. |
Write the locus of the points equidistace from the two given points |
| Answer» {tex}\\style{font-family:Tahoma}{\\style{font-size:8px}{\\begin{array}{l}Let\\;P(x,y,z)\\;be\\;any\\;point\\;which\\;is\\;equidis\\tan t\\;from\\;A(0,2,3)\\;and\\;B\\;(2,\\;-2,1),\\\\PA\\;=\\;PB\\\\\\Rightarrow PA^2\\;=\\;PB^2\\\\\\Rightarrow\\sqrt{\\left(x-0\\right)^2\\;+\\left(y-2\\right)^2+\\left(z-3\\right)^2}\\;=\\sqrt{\\left(x-2\\right)^2\\;+\\left(y+2\\right)^2+\\left(z-1\\right)^2}\\\\\\Rightarrow\\;4x\\;-\\;8y\\;-\\;4z\\;+4\\;=\\;0\\;or\\;x\\;-\\;2y\\;-\\;z\\;+1\\;=\\;0\\\\Hence\\;the\\;required\\;locus\\;is\\;x\\;-\\;2y\\;-\\;z+1\\;=\\;0\\end{array}}}{/tex} | |