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NDA 2025 Maths · Mathematics · Conic Sections · medium

If the parabola y^2=4ax passes through the point (2,4), then its focus is

Single correct option

If the parabola y2=4axy^2=4ax passes through the point (2,4)(2,4), then its focus is
  1. A. (4,0)(4,0)
  2. B. (1,0)(1,0)
  3. C. (0,2)(0,2)
  4. D. (2,0)(2,0)
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Answer: (D) (2,0)(2,0)

Substituting (2,4)(2,4): 16=4a⋅216=4a\cdot2, so a=2a=2. The focus of y2=4axy^2=4ax is (a,0)=(2,0)(a,0)=(2,0). The point (4,0)(4,0) uses 2a2a, (1,0)(1,0) takes a=12⋅2a=\frac12\cdot2 wrongly from y2=4xy^2=4x by guessing, and (0,2)(0,2) is the focus of x2=4ayx^2=4ay, a parabola with a vertical axis.
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