1.

If the distances of `P(x, y)` from `A(5,1) and B(-1, 5)` are equal, then prove that `3x=2y.

Answer» Since, `P(x,y)` is equidistant from `A(5,1) and B( -1, 5)`.
therefore`" "PA=PB`
`rArr" "sqrt ((x- 5)^(2)+(y-1)^(2))=sqrt((x+1)^(2)+(y-5)^(2))" "` (by using distance formula)
Squaring both sides, we get
` " "(x-5)^(2)+(y -1)^(2)=(x+1)^(2)+(y-5)^(2)`
`rArr " "x^(2)-10x+25+y^(2)-2y+1=x+2x+1+y^(2)-10y+25`
`" "-1 0x-2x=-10y+2y rArr" "12x=8y`
`rArr" "3x=2y`


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