Q.
The locus of the centre of a circle of radius 3 which rolls on the outside of the circle x2+y2+3x−6y−9=0 is:
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a
x2+y2+3x−6y+15=0
b
x2+y2+3x−6y+5=0
c
x2+y2+3x−6y+29/4=0
d
x2+y2+3x−6y−45=0
answer is D.
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Detailed Solution
For the given circle, the centre is (−3/2,3) and radius =(9/4+9+9)=9/2 . Obviously the locus of the centre of the circle which rolls is also a circle having the same centre (−3/2,3) and radius =(9/2)+3=15/2 .∴ the required locus is (x+3/2)2+(y−3)2=(15/2)2 or x2+y2+3x−6y−45=0 .
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