Polar coordinates? Still not bad!

Geometry Level 3

Let b, d>0. The locus of all points P ( r , θ ) P(r,\theta) for which the line OP (where O is the origin) cuts the line r s i n θ = b r\ sin\theta=b in Q such that PQ=d.

Note :This question is a part of set KVPY 2014 SB

( r ± d ) c o s θ = b (r\pm d)cos\theta=b ( r d ) c o s θ = b (r-d)cos\theta=b ( r ± d ) s i n θ = b (r\pm d)sin\theta=b ( r d ) s i n θ = b (r-d)sin\theta=b

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