Write the locus of the points …
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Posted by Ravi Jain 6 years, 6 months ago
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Sia ? 6 years, 6 months ago
{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}
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