If P = (1, 0),Q = (-1, 0),and R = (2, 0) are | vedclass

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(D) Let $S = (x, y)$ be a point on the locus.Given points are $P = (1, 0)$,$Q = (-1, 0)$,and $R = (2, 0)$.The given relation is $SQ^2 + SR^2 = 2 SP^2$

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a straight line parallel to $y$-axis

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(D) Let $S = (x, y)$ be a point on the locus.Given points are $P = (1, 0)$,$Q = (-1, 0)$,and $R = (2, 0)$.The given relation is $SQ^2 + SR^2 = 2 SP^2$.Substituting the coordinates,we get:$((x + 1)^2 + y^2) + ((x - 2)^2 + y^2) = 2((x - 1)^2 + y^2)$Expanding the terms:$(x^2 + 2x + 1 + y^2) + (x^2 - 4x + 4 + y^2) = 2(x^2 - 2x + 1 + y^2)$$2x^2 + 2y^2 - 2x + 5 = 2x^2 + 2y^2 - 4x + 2$Subtracting $2x^2 + 2y^2$ from both sides:$-2x + 5 = -4x + 2$$2x = -3$$x = -3/2$This represents a straight line parallel to the $y$-axis.

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

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