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NDA 2020 Maths · Mathematics · Conic Sections · easy

The directrix of the parabola y^2=4ax is the line x=-a. 2. The focus of the parabola y^2=4ax lies on its directrix.

Single correct option

Consider the following statements:
1. The directrix of the parabola y2=4axy^2=4ax is the line x=−ax=-a.
2. The focus of the parabola y2=4axy^2=4ax lies on its directrix.
Which of the statements 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

For y2=4axy^2=4ax the focus is (a,0)(a,0) and the directrix is x=−ax=-a, so statement 1 is correct. The focus is at distance 2a2a from the directrix and never lies on it, otherwise the defining condition (distance from the focus equals distance from the directrix) would give a degenerate locus, a line. Hence statement 2 is incorrect. Only statement 1 is correct.
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Original question written in the NDA 2020 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