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Question

Find the centre and the radius of the spherex2+y2+z2+2x−4y−6z+5=0, & 2x2+2y2+2z2−2x+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=3Sphere : x2+y2+z2−2x−4y−6z+5=0⇒(x2−2x+1)+(y2−4y+4)+(z2−6z+9)=9⇒(x−1)2+(y−2)2+(z−3)2=32∴ Centre = (1,2,3) radius = 3Sphere : 2x2+2y2+2z2−2x+4y+2z+3=0⇒x2+y2+z2−x+2y+z+32=0⇒(x2−x+14)+(y2+2y+1)+(z2+z+14)=9⇒(x−12)2+(y+1)2+(z+12)2=9∴ Centre = (12,−1,−12) radius = 3

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