Straight Line and Pair of Straight Lines 1 Question 38
38. If $P=(1,0), Q=(-1,0)$ and $R=(2,0)$ are three given points, then locus of the points satisfying the relation $S Q^{2}+S R^{2}=2 S P^{2}$, is
$(1988,2 M)$
(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
Show Answer
Solution:
- Let the coordinate of $S$ be $(x, y)$.
$$ \begin{array}{cc} \because & S Q^{2}+S R^{2}=2 S P^{2} \\ \Rightarrow & (x+1)^{2}+y^{2}+(x-2)^{2}+y^{2}=2\left[(x-1)^{2}+y^{2}\right] \\ \Rightarrow & x^{2}+2 x+1+y^{2}+x^{2}-4 x+4+y^{2}=2\left(x^{2}-2 x+1+y^{2}\right) \\ \Rightarrow & 2 x+3=0 \Rightarrow x=-\frac{3}{2} \end{array} $$
Hence, it is a straight line parallel to $Y$-axis.
