Question

If $P(1,0),Q(-1,0),R(2,0)$ are three given points, then locus of $S$ satisfying the relation $(SQ{)}^2+(SR{)}^2=2(SP{)}^2$ is

• A. a straight line parallel to the $x$-axis
• B. a parabola whose vertex at origin
• C. a straight line parallel to $y$-axis
• D. a circle centred at $(0,0)$.

Answer 1

Answer: (C)

a straight line parallel to $y$-axis

Let $S(x,y)$ and $P(1,0),Q(-1,0),R(2,0)$ are given points
$\therefore {\left(SQ\right)}^2+{\left(SR\right)}^2=2{\left(SP\right)}^2$
$\Rightarrow {(x+1)}^2+y^2+{(x-2)}^2+y^2=2[{(x-1)}^2+y^2]$
$\Rightarrow 2x^2+2y^2+2x-4x+5=2x^2+2y^2-4x+2$
$\Rightarrow 2x+3=0$
which is a straight line parallel to $y$-axis.
Hence, the option C is correct answer.