wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

A variable plane remains at constant distance p from the origin. If it meets coordinates axes at points A,B,C then the locus of the centroid of ABC is

A
x2+y2+z2=9p2
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
x3+y3+z3=9p3
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
x2+y2+z2=9p2
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
x3+y3+z3=9p3
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is A x2+y2+z2=9p2

Let the variable plane be xa+yb+zc=1

A=(a,0,0),B=(0,b,0),C=(0,0,c)

Let G(α,β,γ) be the centroid of ABC

α=a3,β=b3,γ=c3 .........(1)

Also given that, distance of plane from origin is p

11a2+1b2+1c2=p

1a2+1b2+1c2=1p2

1α2+1β2+1γ2=9p2 using (1)

Hence, required locus of G(α,β,γ) is,

1x2+1y2+1z2=9p2

i.e. x2+y2+z2=9p2


flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Straight Line
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon