First slide

Equation of line in Straight lines

Question

If $P (1, 0), Q (- 1, 0)$ and $R (2, 0)$ are three given points, then the locus of point S satisfying the relation $S Q^{2} + S R^{2} = 2 S P^{2}$ , is

Moderate

A

a straight line parallel to x-axis
B

circle through origin
C

circle with centre at the origin
D

a straight line parallel to y-axi

Solution

Let the coordinates of S be (h, k). Then,
$\begin{array}{l} S Q^{2} \cdot S R^{-} = 2 S P^{2} \\ \Rightarrow (h + 1)^{2} + k^{2} + (h - 2)^{2} + k^{2} = 2 [(h - 1)^{2} + k^{2}] \\ - 2 h + 5 = - 4 h + 2 \\ \Rightarrow 2 h + 3 = 0 \end{array}$
Hence, locus of $(h, k)$ is, $2 x + 3 = 0$ which is a straight line
parallel to y-axis.

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