JEE AdvancedHardQuestion 390009
Question
The foot of perpendicular from focus (a, 0) to the tangent ty = x + at² is:
- A(0, at) on the tangent at vertexCorrect
- B(a, 0) itself
- C(at², 2at)
- 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).