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NDA 2019 Maths · Mathematics · Conic Sections · easy

A point on the parabola y^2=8x lies at a distance of 6 units from the focus. Its coordinates are

Single correct option

A point on the parabola y2=8xy^2=8x lies at a distance of 66 units from the focus. Its coordinates are
  1. A. (4,±4)(4,\pm4)
  2. B. (2,±4)(2,\pm4)
  3. C. (6,±43)(6,\pm4\sqrt3)
  4. D. (4,±42)(4,\pm4\sqrt2)
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Answer: (D) (4,±42)(4,\pm4\sqrt2)

For y2=8xy^2=8x we have a=2a=2 and the focus is (2,0)(2,0). The focal distance of (x,y)(x,y) is x+a=x+2=6x+a=x+2=6, so x=4x=4 and y2=32y^2=32, i.e. y=±42y=\pm4\sqrt2. The point (2,±4)(2,\pm4) is the end of the latus rectum, at distance 44 from the focus.
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Original question written in the NDA 2019 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