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# I have a doubt in approaching this math problem

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 :- $(a)4$ $(b)8$ $(c)2$ $(d)10$

Pls post the solution in DETAIL....

Note by Parag Zode
2 years, 7 months ago

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y 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 · 2 years, 7 months ago