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NDA 2017 Maths · Mathematics · Circles · medium

The line y=2x passes through the centre of the circle x^2+y^2-2x-4y+1=0. 2. The origin lies inside the circle x^2+y^2-6x-8y+9=0.

Single correct option

Consider the following statements:
1. The line y=2xy=2x passes through the centre of the circle x2+y2−2x−4y+1=0x^2+y^2-2x-4y+1=0.
2. The origin lies inside the circle x2+y2−6x−8y+9=0x^2+y^2-6x-8y+9=0.
Which of the statements given above is/are correct?
  1. A. 11 only
  2. B. 22 only
  3. C. Both 11 and 22
  4. D. Neither 11 nor 22
Show answer and solution

Answer: (A) 11 only

1: the centre is (1,2)(1,2), which satisfies y=2xy=2x, so it is correct. 2: at the origin the expression equals 9>09>0, so the origin lies outside the circle (inside would need a negative value). Only statement 1 is correct.
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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