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The point 'p' moves so that it is always a distance of 2 from the fixed point C=(2,b).find 'b' if the locus of 'p' passes through (1,0) and (3,0).



Let the point be P(x,y)
given that the distance of this point P from fixed point C(2,b) is always 2 unit 
therefore by distance formula
 \sqrt{ (x-2)^{2}+ (y-b)^{2}}=2
 (x-2)^{2}+( y-b)^{2}=4    x^{2} +4-4x+ y^{2}+ b^{2}-2by=4

 x^{2} + y^{2} -4x-2by+ b^{2} =0
since this passes through (1,0) and (3,0)
therefore x=1 y=0
       b=√3 answer.....
then you put x=3 y=0 then also the answer is b=√3
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