1.

Find the relation between x and y such that the point P (x,y) is equidistant from the points `A(1,4)and B(-1,2).`

Answer» We have
`PA = PB rArr PA^(2) = PB^(2)`
`rArr (x-1)^(2) + (y-4)^(2) =(x+1)^(2) + (y-2)^(2)`
`rArr x^(2) + y^(2) - 2x-8y+17 = x^(2) + y^(2) +2x -4y +5`
`rArr 4x+ 4y- 12 =0 rArr x+ y = 3 rArr y = 3-x`
Hence, y = 3-x is the desired relation between x and y.


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