A circle C of radius 2 units rolls inside the ring of the circle x2+y2+8x−2y−19=0. Then the locus of the centre of C
A
x2+y2+8x−2y−47=0
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B
x2+y2+8x−2y−1=0
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C
x2+y2+8x−2y+1=0
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D
x2+y2−8x+2y+1=0
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Solution
The correct option is Bx2+y2+8x−2y+1=0
S1:x2+y2+8x−2y−19=0 C1=(−4,1) and r1=6 Let P(x,y) is a centre of the circle C. Distance PC1=6−2=4 √(x+4)2+(y−1)2=4 x2+y2+8x−2y+17−16=0 ⇒x2+y2+8x−2y+1=0