Question

4.
The locus of a point whose sum of squares of whose distances from the axes is p’, is ?​

Answer 1

Answer:

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Answer 2

Step-by-step explanation:

Given, planes are x−z=0,x−2y+z=0 and x+y+z=0

Let the point whose locus is required be P(α,β,γ).

According to the question, 

2∣α−γ∣2+6∣α−2β+γ∣2+3∣α+β+γ∣2=36⇒3(α2+β2+γ2)+α2+4β2+γ2−4αβ−4βγ+2αγ+2(α2+β2+γ2+2αβ+2βγ+2αγ)=36×6⇒6α2+6β2+6γ2=36×6⇒α2+β2+γ2=36

Hence, the equation of required locus is x2+y2+z2