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NDA 2017 Maths · Mathematics · Straight Lines · medium

The line through (1,2) whose non-zero intercepts on the axes are equal in magnitude but opposite in sign is

Single correct option

The line through (1,2)(1,2) whose non-zero intercepts on the axes are equal in magnitude but opposite in sign is
  1. A. x+y=3x+y=3
  2. B. 2x−y=02x-y=0
  3. C. x−y+1=0x-y+1=0
  4. D. x−2y+3=0x-2y+3=0
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Answer: (C) x−y+1=0x-y+1=0

Intercepts aa and −a-a give xa−ya=1\frac xa-\frac ya=1, i.e. x−y=ax-y=a. Passing through (1,2)(1,2) gives a=−1a=-1, so x−y+1=0x-y+1=0. The line x+y=3x+y=3 has equal intercepts of the same sign, and 2x−y=02x-y=0 passes through the origin (zero intercepts); all three wrong lines pass through (1,2)(1,2), so checking the point alone is not enough.
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Original question written in the NDA 2017 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