two points P and Q lying on side of a radial line OPQ are said to be inverse points with respect to a circle x²+y²=a² whose centre is O provided OP.OQ=a² if Possible lies on the line 3x+4y=0, the locus of Q is :

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Sum of series 2[n/2] ! [n/2]!/ n! [2Co-2C2+3C2....+[-1]^n[n+1]2Cn] where n is an even positive integer. Kindly provide solution of this question and how to generalise this. How do we know that which expansion will give this?