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

$S Q^{2} + S R^{2} = 2 S P^{2}$ is

A straight line parallel to x-axis

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A circle through origin

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A circle with centre at the origin

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A straight line parallel to y-axis

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Solution

The correct option is D
A straight line parallel to y-axis

Let S(x, y), then

$(x + 1)^{2} + y^{2} + (x - 2)^{2} + y^{2} = 2 [(x - 1)^{2} + y^{2}]$

$\Rightarrow$ 2x +1 + 4 - 4x = - 4x + 2 $\Rightarrow$ x = - $\frac{3}{2}$

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

Suggest Corrections

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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

$S Q^{2} + S R^{2} = 2 S P^{2}$ is

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

$S Q^{2} + S R^{2} = 2 S P^{2}$ is

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