1.

Find the equation of the set of all points which are twice as far from (3, 2) as from (1, 1).

Answer» Let `P(x, y)` be a point and let `A( 3,2) and B(1,1)` be two other points on the plane, such that
`" " PA=2PB`
`rArr" "sqrt((x-3)^(2)+(y-2)^(2))=2sqrt((x-1)^(2)+(y -1)^(2))`
Squaring both sides, we have
`" "x^(2)-6x+9+y^(2)-4y+4=4(x^(2)-2x+1+y^(2)-2y+1)`
`rArr" "3x^(2)+3y^(2)-2x-4y-5=0`
Which is the required equation.


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