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If $P (1, 0), Q (- 1, 0)$ and $R (2, 0)$ are 3 given points then locus of points S satisfying the relation $S Q^{2} + S R^{2} = 2 S P^{2}$ is

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Straight line parallel to X - axis

A circle passing through origin

A circle with center at origin

A straight line parallel to Y - axis

answer is D.

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Detailed Solution

$P = (1, 0) Q = (- 1, 0) R (2, 0) S = (h, k) {(h + 1)}^{2} + {(k - 0)}^{2} + {(h - 2)}^{2} + {(k - 0)}^{2} = 2 [{(h - 1)}^{2} + k^{2}]$

$\Rightarrow 2 h + 3 = 0 \Rightarrow$ line parallel to Y-axis

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