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NDA 2016 Maths · Mathematics · Circles · medium

The circles x^2+y^2=4 and (x-3)^2+y^2=1 touch each other externally. 2. The line y=x+3 is a tangent to the circle x^2+y^2=9.

Single correct option

Consider the following statements:
1. The circles x2+y2=4x^2+y^2=4 and (x−3)2+y2=1(x-3)^2+y^2=1 touch each other externally.
2. The line y=x+3y=x+3 is a tangent to the circle x2+y2=9x^2+y^2=9.
Which of the statements given above is/are correct?
  1. A. 1 only
  2. B. 2 only
  3. C. Both 1 and 2
  4. D. Neither 1 nor 2
Show answer and solution

Answer: (A) 1 only

The centres are (0,0)(0,0) and (3,0)(3,0), with distance 3=2+13=2+1 (sum of radii), so the circles touch externally and statement 1 is true. The distance of the origin from x−y+3=0x-y+3=0 is 3/2≠33/\sqrt2\ne3, so the line is not a tangent and statement 2 is false.
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Original question written in the NDA 2016 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