VITEEE 2016 Paper

Let A= (a, 0,0), B = (0, b, 0), C = (0,0, c), then equation of the plane is

x

a

+

y

b

+

z

c

= 1
Its distance from the origin,

1

a2

+

1

b2

+

1

c2

=

1

p2

... (i)
If (x, y, z) be centroid of δ ABC, then
x =

a

3

, y =

b

3

, z =

c

3

... (ii)
Eliminating a,b,c from (i) and (ii) required locus is
x−2+y−2+z−2 = 9p−2