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

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a straight line parallel to x-axis

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Correct option is D

Let the coordinates of S be (h, k). Then, SQ2⋅SR−=2SP2⇒ (h+1)2+k2+(h−2)2+k2=2(h−1)2+k2−2h+5=−4h+2⇒ 2h+3=0 Hence, locus of (h,k) is, 2x+3=0 which is a straight line parallel to y-axis.

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If P(1,0),Q(−1,0) and R(2,0) are three given points, then the locus of point S satisfying the relation SQ2+SR2=2SP2, is

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