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Question

If P(1,0),Q(1,0),R(2,0) are three given points, then locus of S satisfying the relation (SQ)2+(SR)2=2(SP)2 is

A
a straight line parallel to the x-axis
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B
a parabola whose vertex at origin
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C
a straight line parallel to y-axis
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D
a circle centred at (0,0).
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Solution

The correct option is B a straight line parallel to y-axis
Let S(x,y) and P(1,0),Q(1,0),R(2,0) are given points
(SQ)2+(SR)2=2(SP)2
(x+1)2+y2+(x2)2+y2=2[(x1)2+y2]
2x2+2y2+2x4x+5=2x2+2y24x+2
2x+3=0
which is a straight line parallel to y-axis.
Hence, the option C is correct answer.

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