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The point A (2,4) is joined to any point P on the circle x^2+y^2=4.The locus of the mid point of AP as p moves on circle is:
let p have coordinates 2cosq, 2sinqnow mid point be (h,k)so, 2h=2+2cosq or h – 1= cosqand 2k= 4+2sinq or k – 2=sinqsquaring and adding, nd replacing h and k by x and y resp,(x – 1)^2+(y – 2)^2= 1 is the reqd locus
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