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Question

Find a relation between x and y such that the point (x,y) is equidistant from the points (7,1) and (3,5).

Solution
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Let P(x,y) be equidistant from the points A(7,1) and B(3,5).
AP=BP
AP2=BP2
(x7)2+(y1)2=(x3)2+(y5)2
x214x+49+y22y+1=x26x+9+y210y+25
xy=2

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