A variable plane at a constant distance p from the origin meets the coordinate axes in points A,B and C respectively.Through these points , planes are drawn parallel to the coordinate planes, show that locus of the point of intersection is `1/x^2+1/y^2+1/z^2=1/p^2`

Explanation

Following is the equation of the plane:

`lx + my + nz = 3p`

The intercepts on the 3 axes are `a=3p/l, b=3p/m, c=3p/n`

The coordinates of the centroid are

`x=a/3=p/l`

`y=b/3=p/m`

`z=c/3=p/n`

Now `1/x^2 + 1/y^2 + 1/z^2`

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