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

The plane 2x−2y+z+12=0 touches the sphere x2+y2+z2−2x−4y+2z−3=0 at the point

A
(1,4,2)
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
(1,4,2)
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
(1,4.2)
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
(1,4,2)
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is A (1,4,2)
Equation of line passing through center of sphere (1,2,1) and perpendicular to the plane of sphere having direction ratios (2,2,1) is
s:x2+y2+z22x4y+2z3=0
And plane x12=y22=z+11=λ
Any point on the line is P(2λ+1,2λ+2,λ1)
This point will lie in the plane, if it satisfies the given equation of the plane such that
2(2λ+1)2(2λ+2)+(λ+1)+12=09λ+9=0
λ=1

404024_252653_ans.PNG

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