Coordinate Geometry Question 79
Question: If P = (1,0), Q =(-1,0) and R =(2,0) are three given points, then the locus of a point S satisfying the relation $ SQ^{2}+SR^{2}=2SP^{2} $ is
[IIT 1988]
Options:
A) A straight line parallel to x-axis
B) A circle through origin
C) A circle with centre at the origin
D) A straight line parallel to y-axis
Show Answer
Answer:
Correct Answer: D
Solution:
Let $ S(x,y), $ then $ {{(x+1)}^{2}}+y^{2}+{{(x-2)}^{2}}+y^{2}=2[{{(x-1)}^{2}}+y^{2}] $
$ \Rightarrow 2x+1+4-4x=-4x+2\Rightarrow x=-\frac{3}{2} $
Hence it is a straight line parallel to y-axis.
BETA
