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 $SQ^{2} + SR^{2} = 2SP^{2}$ 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

Answer: (D)

A straight line parallel to y-axis

Answer 2

Let $S ( x , y )$ then

$( x + 1 ) ^ { 2 } + y ^ { 2 } + ( x - 2 ) ^ { 2 } + y ^ { 2 } = 2 \left[ ( x - 1 ) ^ { 2 } + y ^ { 2 } \right]$ $\Rightarrow 2 x + 1 + 4 - 4 x = - 4 x + 2 \Rightarrow x = - \frac { 3 } { 2 }$

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