CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

Find the equation of a sphere, whose centre is (1,1,1) and radius is 5 units


A

x2+y2+z2xyz=5

No worries! We‘ve got your back. Try BYJU‘S free classes today!
B

x2+y2+z2xx2y2z=5

No worries! We‘ve got your back. Try BYJU‘S free classes today!
C

x2+y2+z2xyz=25

No worries! We‘ve got your back. Try BYJU‘S free classes today!
D

x2+y2+z22x2y2z=22

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
Open in App
Solution

The correct option is D

x2+y2+z22x2y2z=22


Sphere can be thought of as a three dimensional extension of a circle. Similar to distance formula and section formula, the equation of sphere has additional terms involving z coordinate. To find the equation of the sphere, let’s consider a general point P(x,y,z) on the sphere. Let the centre of the sphere be O(1,1,1). We are given that the radius is 5 units.

Distance of P from O will be equal to the radius, that is 5 units. Using distance formula, we get

PO=(x1)2+(y1)2+(z1)2=5(x1)2+(y1)2+(z1)2=25x2+y2+z22x2y2z=22
This is the equation of the sphere with centre (1,1,1) and radius 5 units


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