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At the point P(16, 16) on the parabola y² = 16x, the tangent and the normal are drawn; they meet the axis of the parabola at A and B respectively. If C is the centre of the circle passing through P, A, B and angle CPB = theta, find a possible value of tan(theta).

1. 2
2. 3
3. 4/3
4. 1/2

Correct answer: 2

Solution

Tangent and normal are perpendicular, so AB is the diameter and C its midpoint; computing the geometry gives tan(theta) = 2 (this is the JEE 2018 answer).

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