Given \(P,Q\) are two points on the curve \[y=log_\dfrac{1}{2}(x-0.5)+log_2\sqrt{4x^2-4x+1}\] ,\(P\) is also lying on the circle \[x^2+y^2=10\]. If \(Q\) lies inside the given circle such that it's abscissa is integer then \[\vec{OP}.\vec{OQ}\] is equal to :- \[(a)4\] \[(b)8\] \[(c)2\] \[(d)10\]

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## Comments

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TopNewesty for first function is always one. solve it also, x>0.5 due to log function

therefore, P=(3,1) by putting y=1 in circle

Q =(1,1) or (2,1)

Write OP= 3i+j, OQ as i+j and 2I+j. Multiply and get a

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