(D) Let the coordinates of point $S$ be $(x, y)$.Given the relation $SQ^2 + SR^2 = 2SP^2$.Substituting the coordinates,we get:$((x + 1)^2 + (y - 0)^2)

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$A$ straight line parallel to $y$-axis

(D) Let the coordinates of point $S$ be $(x, y)$.Given the relation $SQ^2 + SR^2 = 2SP^2$.Substituting the coordinates,we get:$((x + 1)^2 + (y - 0)^2) + ((x - 2)^2 + (y - 0)^2) = 2((x - 1)^2 + (y - 0)^2)$$(x^2 + 2x + 1 + y^2) + (x^2 - 4x + 4 + y^2) = 2(x^2 - 2x + 1 + y^2)$$2x^2 - 2x + 5 + 2y^2 = 2x^2 - 4x + 2 + 2y^2$$-2x + 5 = -4x + 2$$2x = -3$$x = -\frac{3}{2}$This represents a straight line parallel to the $y$-axis.

Class 11 Mathematics 10-1.Circle and System of Circles Locus Related Problem

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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

IIT 1988 All IIT

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$A$ 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

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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

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From a point $P$ on the circle $x^2+y^2=4$,two tangents are drawn to the circle $x^2+y^2-6x-6y+14=0$. If $A$ and $B$ are the points of contact of those lines,then the locus of the centre of the circle passing through the points $P, A$ and $B$ is

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