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Question

If P=(1,0),Q=(−1,0),R=(2,0) are 3 given points, then the locus of the point S satisfying the relation SQ2+SR2=2SP2 is

A
a straight line parallel to the x-axis
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B
circle through the origin
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C
circle with centre at the origin
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D
a straight line parallel to the y-axis.
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Solution

The correct option is D a straight line parallel to the y-axis.
Given points
P(1,0),Q(1,0),R(2,0)
Let point S(x,y)
SQ2+SR2=2SP2
(x+1)2+y2+(x2)2+y2=2((x1)2+y2)
x2+1+2x+y2+x2+44x+y2=2(x2+12x+y2)
2x22x+2y2+5=2x2+24x+2y2
2x+5=24x
2x=3x=32
Line x=32 represents a line which is parallel to y-axis

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