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NDA 2023 Maths · Mathematics · Conic Sections · medium

The equation x^2+y^2+2x+2y+2=0 represents a point circle. 2. The eccentricity of every parabola is 1.

Single correct option

Consider the following statements:
1. The equation x2+y2+2x+2y+2=0x^2+y^2+2x+2y+2=0 represents a point circle.
2. The eccentricity of every parabola is 11.
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: (C) Both 1 and 2

For the first equation g=f=1g=f=1, c=2c=2 and r2=g2+f2−c=0r^2=g^2+f^2-c=0, so it represents the single point (−1,−1)(-1,-1) and Statement 1 is correct. A parabola is the locus with distance ratio to focus and directrix equal to 11, so e=1e=1 for every parabola and Statement 2 is also correct.
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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