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NDA 2023 Maths · Mathematics · Conic Sections · medium

A parabola with vertex at the origin and axis along the y-axis passes through the point (4,-2). Its equation is

Single correct option

A parabola with vertex at the origin and axis along the yy-axis passes through the point (4,−2)(4,-2). Its equation is
  1. A. x2=8yx^2=8y
  2. B. y2=8xy^2=8x
  3. C. x2=−8yx^2=-8y
  4. D. x2=−32yx^2=-32y
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Answer: (C) x2=−8yx^2=-8y

The form is x2=kyx^2=ky. Substituting (4,−2)(4,-2) gives 16=−2k16=-2k, so k=−8k=-8 and the equation is x2=−8yx^2=-8y. Option y2=8xy^2=8x has its axis along the xx-axis, and x2=8yx^2=8y opens upward so it cannot contain a point with negative yy.
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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