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Q.

P is a point which moves in the xy plane such that the point P nearer to the centre of a square then any of the sides. The four vertices of the square are  (±a,±a). The region in which P will move is bounded by parts of parabolas of which one has the equation

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a

y2=a2+2ax

b

x2=a2+2ay

c

y2+2ax=a2

d

All of these

answer is D.

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Detailed Solution

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If  P(x,y)  thenx2+y2<|ax|,x2+y2<|a+x|x2+y2<|ay|,x2+y2<|a+y|Squaring then we get the region bounded by the curvesx2+y2=(ax)2,x2+y2=(a+x)2x2+y2=(ay)2,x2+y2=(a+y)2

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