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If P= (1,0);Q=(-1,0) & R= (2,0) are thre...

If `P= (1,0);Q=(-1,0) & R= (2,0)` are three given points, then the locus of the points S satisfying the relation, `SQ^2 + SR^2 =2SP^2` is - (a)a straight line parallel to x-axis (b) A circle through origin (c) A circle with center at the origin (d)a straight line parallel to y-axis

A

a straight line parallel to `X` -axis

B

a circle passing through the origin

C

a circle with the centre at the origin

D

a straight line parallel to `Y`-axis

Text Solution

Verified by Experts

Let the coordinate of `S` be `(x,y)`.
`:' SQ^(2)+SR^(2)=2SP^(2)`
`implies(x+1)^(2)+y^(2)+(x-2)^(2)+y^(2)=2[(x-1)^(2)+y^(2)]`
`impliesx^(2)+2x+1+y^(2)+x^(2)-4x+4+y^(2)=2(x^(2)-2x+1+y^(2))`
`implies2x+3=0impliesx=-(3)/(2)`
Hence, it is a straight line parallel to `Y`-axis.
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