The locus of the point `P(x,y)` satisfying the relation `sqrt((x-3)^2+(y-1)^2)+sqrt((x+3)^2+(y-1)^2)=6`, is

Options

A. point
B. pair of coincident straight lines
C. circle
D. ellipse

Answer

B

Explanation

Given , `sqrt((x-3)^2+(y-1)^2)+sqrt((x+3)^2+(y-1)^2)=6`
`rArr sqrt((x-3)^2+(y-1)^2)=6-sqrt((x+3)^2+(y-1)^2)`
`rArr (x-3)^2+(y-1)^2=36+{(x+3)^2+(y-1)^2}-12sqrt((x+3)^2+(y-1)^2)`
`rArr x^2+9-6x+y^2+1-2y=36+x^2+9+6x+y^2+1-2y-12sqrt((x+3)^2+(y-1)^2)`
`rArr -12x-36=-12sqrt((x+3)^2+(y-1)^2)`
`rArr 12(x+3)=12sqrt((x+3)^2+(y-1)^2)`
`rArr x+3=sqrt((x+3)^2+(y-1)^2)`
`rArr (x+3)^2=(x+3)^2+(y-1)^2`
`rArr x^2+9+6x=x^2+9+6x+y^2+1-2y`
`rArr y^2-2y+1=0`
`rArr (y-1)(y-1)=0`
`therefore` Pair of coincident straight lines .