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rectangular cartensian co-ordinates — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSrectangular cartensian co-ordinates1 Mark
MCQ
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 $S{Q^2} + S{R^2} = 2S{P^2}$ is
  • A
    A straight line parallel to $x$-axis
  • B
    A circle through origin
  • C
    A circle with centre at the origin
  • ✓
    A straight line parallel to $y$-axis
✓

Answer

Correct option: D.
A straight line parallel to $y$-axis
d
(d) 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.

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