If P = (1, 0) ; Q = (-1, 0) ,,ane,, R = (2, 0) are three given points, then locus of points S satisf

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9.Straight Line

normal

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

A

a straight line parallel to $x-$ axis

B

a circle passing through the origin

C

a circle with the centre at the origin

D

a straight line parallel to $y-$ axis .

Solution

Let $S(x, y)$ and $P(1,0), Q(-1,0), R(2,0)$ are given points

$\therefore(S Q)^{2}+(S R)^{2}=2(S P)^{2}$

$\Rightarrow(x+1)^{2}+y^{2}+(x-2)^{2}+y^{2}=2\left[(x-1)^{2}+y^{2}\right]$

$\Rightarrow 2 x^{2}+2 y^{2}+2 x-4 x+5=2 x^{2}+2 y^{2}-4 x+2$

$\Rightarrow 2 x+3=0$

which is a straight line parallel to $y$ -axis.

Standard 11

Mathematics

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(JEE MAIN-2024)