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NDA 2021 Maths · Mathematics · Circles · hard

The line 3x+4y=25 cuts the circle x^2+y^2=25 at two distinct points. 2. x^2+y^2+2x+2y+5=0 represents a real circle.

Single correct option

Which of the statements is/are correct? 1. The line 3x+4y=253x+4y=25 cuts the circle x2+y2=25x^2+y^2=25 at two distinct points. 2. x2+y2+2x+2y+5=0x^2+y^2+2x+2y+5=0 represents a real circle.
  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: (D) Neither 1 nor 2

The distance of the centre from the line is 25/5=525/5=5, equal to the radius, so the line is a tangent and touches the circle at one point; statement 1 is false. For statement 2, g=f=1g=f=1 and c=5c=5, so r2=g2+f2−c=−3<0r^2=g^2+f^2-c=-3<0: the circle is imaginary and statement 2 is false.
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Original question written in the NDA 2021 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