Q.

A chord AB drawn from the point A(0,3) on circle x2+4x+(y-3)2=0 meets M in such a way that AM=2AB , then the locus of point M will be

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a

straight line

b

circle

c

parabola

d

None of these

answer is B.

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Detailed Solution

Let Mx,y be any point on the locusHence, B is the midpoint of AMB=x2,y+32, it lies on the circlex22+4x2+y+32−32=0x2+8x+y−32=0it is an equation of circle
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A chord AB drawn from the point A(0,3) on circle x2+4x+(y-3)2=0 meets M in such a way that AM=2AB , then the locus of point M will be