JEE Mathematics · Hard

Parabola: JEE Advanced MCQ

Solve this quality-checked JEE multiple-choice question, then review the correct answer and explanation.

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JEE AdvancedHardQuestion 390009

Question

The foot of perpendicular from focus (a, 0) to the tangent ty = x + at² is:
  1. A
    (0, at) on the tangent at vertex
    Correct
  2. B
    (a, 0) itself
  3. C
    (at², 2at)
  4. D
    (−at², 0)

Correct answer

(0, at) on the tangent at vertex

Explanation

The foot of the perpendicular from the focus (a, 0) to any tangent ty = x + at² lies on the tangent at the vertex (the y-axis, x = 0). Substituting x = 0 in ty = x + at²: y = at. So foot = (0, at), which lies on x = 0 (tangent at vertex).