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If the distances of P(x, y) from A(5,1) ...

If the distances of `P(x, y)` from `A(5,1) and B(-1, 5)` are equal , then ,

A

`2x=3y`

B

`2x=5y`

C

`3x=2y`

D

`5x=2y`

Text Solution

Verified by Experts

The correct Answer is:
C
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^2+2x+1+y^(2)-10y+25`
`rArr " -1 0x-2x=-10y+2y`
`rArr" "12x=8y`
`rArr" "3x=2y`
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