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CGP EDU Academic Team
Published on: August 13, 2026
Find the locus of a point, the sum of squares of whose distances from the planes: x –z = 0, x –2y + z = 0 and
x + y + z = 0 is 36
Text Solution
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Sol. Given planes are:
x –z = 0, x –2y + z = 0, x + y + z = 0
Let the point whose locus is required be P( α, β, γ ). According to question
+ 
+ 
= 36
or 3( α 2 + γ 2 –2 αγ ) + α 2 + 4 β 2 + γ 2 –4 αβ –4 βγ + 2 αγ
+2( α 2 + β 2 + γ 2 + 2 αβ + 2 βγ + 2 αγ ) = 36 × 6
or 6 α 2 + 6 β 2 + 6 γ 2 = 36 × 6 or α 2 + β 2 + γ 2 = 36
Hence, the required equation of locus is x 2 + y 2 + z 2 = 36
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