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Given four points P1,P2,P3a n dP4 on the...

Given four points `P_1,P_2,P_3a n dP_4` on the coordinate plane with origin `O` which satisfy the condition `( vec (O P))_(n-1)+( vec(O P))_(n+1)=3/2 vec (O P)_(n)` (i) If P1 and P2 lie on the curve xy=1 , then prove that P3 does not lie on the curve (ii) If P1,P2,P3 lie on a circle `x^2+y^2=1`, then prove that P4 also lies on this circle.

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