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9.Straight Line
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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