SATHEE: Straight Line and Pair of Straight Lines 1 Question 38

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

(d) a straight line parallel to $Y$ -axis

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Solution:

Let the coordinate of $S$ be $(x, y)$ .

$\begin{array}{cc} ∵ & S Q^{2} + S R^{2} = 2 S P^{2} \\ \Rightarrow & (x + 1)^{2} + y^{2} + (x - 2)^{2} + y^{2} = 2 [(x - 1)^{2} + y^{2}] \\ \Rightarrow & x^{2} + 2 x + 1 + y^{2} + x^{2} - 4 x + 4 + y^{2} = 2 (x^{2} - 2 x + 1 + y^{2}) \\ \Rightarrow & 2 x + 3 = 0 \Rightarrow x = - \frac{3}{2} \end{array}$

Hence, it is a straight line parallel to $Y$ -axis.

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

Solution:

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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 SQ2+SR2=2SP2, is

Solution:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

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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