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NDA 2024 Maths · Mathematics · Conic Sections · medium

Consider the parabola y^2=8x. 1. Its focus is (2,0). 2. Its directrix is the line x=2.

Single correct option

Consider the parabola y2=8xy^2=8x.
1. Its focus is (2,0)(2,0).
2. Its directrix is the line x=2x=2.
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

Comparing with y2=4axy^2=4ax gives 4a=84a=8, so a=2a=2. The focus is (a,0)=(2,0)(a,0)=(2,0), so statement 1 is true. The directrix is x=−a=−2x=-a=-2, not x=2x=2, so statement 2 is false. Trap: the directrix lies on the opposite side of the vertex from the focus.
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Original question written in the NDA 2024 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