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If \mathrm{P \equiv(1,0), Q \equiv(-1,0)} and \mathrm{R \equiv(2,0)} are 3 given points, then locus of the point S satisfying the relation \mathrm{S Q^{2}+S R^{2}=2 S P^{2}} is

Option: 1

a straight line parallel to x-axis


Option: 2

 a circle passing through the origin.


Option: 3

A circle with the centre at the origin


Option: 4

a straight line parallel to y-axis.


Answers (1)

best_answer

 Let the point \mathrm{S} be (\mathrm{h}, \mathrm{k}).  According to given condition

\mathrm{\left\{(h+1)^{2}+k^{2}\right\}+\left\{(h-2)^{2}+k^{2}\right\}=2\left\{(h-1)^{2}+k^{2}\right\}}

\mathrm{\Rightarrow 2 \mathrm{~h}+3=0}  which is a straight line parallel to \mathrm{\mathrm{y}}-axis.

Hence (D) is the correct answer.

 

Posted by

Divya Prakash Singh

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