Question

24) If P = (1,0); Q = (-1,0) & R = (2,0) are three given points, then locus of the points S satisfying the relation,
SQ² + SR² = 2 SP² is -

(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

Answer 1

Dear student

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

Then, according to given condition SQ² + SR² = 2SP²

Since the coordinates are given, we substitute them in the condition and obtain

(x+1)² + y² + (x-2)² + y² = 2[(x-1)² + y²]

This gives, x² + 2x + 1 + y² + x² - 4x + 4 + y² = 2 (x² + 1 - 2x + y²)

This yields 2x + 3 = 0.

Hence, x = -3/2.

Hence, the line satisfying the given condition is a straight line parallel to y-axis.
Regards