3
Question
The equation of the sphere touching the three co-ordinate planes is
[AMU 2002]
The equation of the sphere touching the three co-ordinate planes is
[AMU 2002]
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Solution
The correct options are
B
C
Given, sphere touching the three co-ordinates planes. So clearly the centre is (a,a,a) and radius is a.
From (x−a)2+(y−b)2+(z−c)2+r2,
∴(x−a)2+(y−a)2+(z−a)2=a2
x2+y2+z2−2ax−2ay−2az+3a2=a2
∴x2+y2+z2−2a(x+y+z)+2a2=0 is the required equation of sphere.
B
C
Given, sphere touching the three co-ordinates planes. So clearly the centre is (a,a,a) and radius is a.
From (x−a)2+(y−b)2+(z−c)2+r2,
∴(x−a)2+(y−a)2+(z−a)2=a2
x2+y2+z2−2ax−2ay−2az+3a2=a2
∴x2+y2+z2−2a(x+y+z)+2a2=0 is the required equation of sphere.