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Locus of Tangent–Focal-Perpendicular Intersection | JEE

JEE Maths question with a full step-by-step solution.

Question
The locus of the point of intersection of any tangent to the parabola y2=4a(x−2)y^2 = 4a(x - 2) with a line perpendicular to it and passing through the focus is:
Ax=2x = 2correct
By=2y = 2
Cx=ax = a
Dx=a+2x = a + 2
Solution
The foot of the perpendicular from the focus to any tangent lies on the tangent at the vertex, and the required intersection is exactly that foot. For y2=4a(x−2)y^2 = 4a(x - 2) the vertex is (2,0)(2, 0), so the locus is the tangent at the vertex, x=2x = 2. Correct answer: (1)
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