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Question

In a right angled isosceles ABC, where A is at origin and side lengths AB and AC are equal to a units. If point B and C are produced to P and Q respectively such that BPCQ=AB2, then the locus of the midpoint of PQ is

A
1x+1y=4a
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B
1x+1y=12a
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C
1x+1y=1a
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D
1x+1y=2a
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