The equation of the sphere concentric with the sphere x2+y2+z2−4x−2y−6z−7=0 and passing through (0,0,0) is :
A
x2+y2+z2−4x−2y−6z=0
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B
x2+y2+z2=0
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C
x2+y2+z2−4x−2y=0
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D
None of these
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Solution
The correct option is Ax2+y2+z2−4x−2y−6z=0 Let the required sphere be x2+y2+z2+2gx+2fy+2wz+d=0 ...(i) Now it is concentric withh x2+y2+z2−4x−2y=6z−7=0 ∴g=−2,f=−1,w=−3 Also (i) passes through (0,0,0) we get d=0 ∴ required sphere is x2+y2+z2−4x−2y−6z=0