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Question

Find the centre and the radius of the sphere
x2+y2+z2+2x4y6z+5=0, & 2x2+2y2+2z22x+4y+2z+3=0.

A
C1=(1,2,3),r1=3,C2=(12,1,12),r2=3
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B
C1=(1,2,3),r1=3,C2=(12,2,12),r2=3
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C
C1=(1,2,3),r1=3,C2=(12,2,12),r2=3
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D
C1=(1,2,3),r1=3,C2=(12,2,12),r2=3
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Solution

The correct option is D C1=(1,2,3),r1=3,C2=(12,1,12),r2=3
Sphere : x2+y2+z22x4y6z+5=0
(x22x+1)+(y24y+4)+(z26z+9)=9
(x1)2+(y2)2+(z3)2=32
Centre = (1,2,3) radius = 3
Sphere : 2x2+2y2+2z22x+4y+2z+3=0
x2+y2+z2x+2y+z+32=0
(x2x+14)+(y2+2y+1)+(z2+z+14)=9
(x12)2+(y+1)2+(z+12)2=9
Centre = (12,1,12) radius = 3

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