Question

If P = (1, 0), Q = (-1, 0) and R = (2, 0) are three given points, then the locus of a point S satisfying the relation

$S{Q}^2+S{R}^2=2S{P}^2$ is

• A. A straight line parallel to x-axis
• B. A circle through origin
• C. A circle with centre at the origin
• D. A straight line parallel to y-axis

Answer 1

The correct option is D

A straight line parallel to y-axis

Let S(x, y), then

$(x+1{)}^2+y^2+(x-2{)}^2+y^2=2\left[\right(x-1{)}^2+y^2]$

$\Rightarrow$ 2x +1 + 4 - 4x = - 4x + 2 $\Rightarrow$ x = -$\frac{3}{2}$

Hence it is a straight line parallel to y-axis.