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NDA 2023 Maths · Mathematics · Straight Lines · medium

The locus of a point which is equidistant from (2,0) and (0,2) is

Single correct option

The locus of a point which is equidistant from (2,0)(2,0) and (0,2)(0,2) is
  1. A. x+y=2x+y=2
  2. B. x+y=0x+y=0
  3. C. y=xy=x
  4. D. x=y+2x=y+2
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Answer: (C) y=xy=x

Equate squared distances: (x−2)2+y2=x2+(y−2)2(x-2)^2+y^2=x^2+(y-2)^2, which simplifies to −4x=−4y-4x=-4y, i.e. y=xy=x. This is the perpendicular bisector of the segment; the line x+y=2x+y=2 is the line through the two points, not the bisector.
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Original question written in the NDA 2023 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake