JEE Advanced Mathematics question

Two tangents to the parabola meet at the point . STATEMENT-1: The tangents are perpendicular to each other. STATEMENT-2: Mutually perpendicular tangents to the parabola meet on the line .

(A)Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1Correct
(B)Statement-1 is True, Statement-2 is True; Statement-2 is *Not* a correct explanation for Statement-1
(C)Statement-1 is True, Statement-2 is False
(D)Statement-1 is False, Statement-2 is True

Answer: (A)

Solution

, so and the directrix is , i.e. . Perpendicular tangents to a parabola meet on its directrix, so Statement-2 is true. The point lies on the directrix; the two tangents from any point of the directrix are perpendicular, so

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Question ID VK-110445