Straight LineMedium
Question
If P = (1,0),Q = (-1,0) and R = (2,0) are three given points, then locus of the points satisfying the relation SQ2 + SR2 = 2SP2 ,is
Options
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 the coordinate of S be (x, y),
∵ SQ2 + SR2 = 2SP2
⇒ (x +1)2 + y2 + (x - 2)2 + y2
= 2[(x +1)2 + y2]
⇒ x2 + 2x +1+ y2 + x2 - 4x + 4 + y2
= 2(x2 - 2x +1+ y2)
⇒ 2x +3 = 0
⇒
Hence, it is a strainght line parallel to y-axis.
∵ SQ2 + SR2 = 2SP2
⇒ (x +1)2 + y2 + (x - 2)2 + y2
= 2[(x +1)2 + y2]
⇒ x2 + 2x +1+ y2 + x2 - 4x + 4 + y2
= 2(x2 - 2x +1+ y2)
⇒ 2x +3 = 0
⇒
Hence, it is a strainght line parallel to y-axis.
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