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A focal chord of the parabola y² = 4ax has length c and lies at perpendicular distance b from the vertex. Which relation holds?

1. a³ = b² c
2. 2a² = bc
3. ac = b²
4. b² c = 4a³

Correct answer: a³ = b² c

Solution

From b = a sin(theta), sin² theta = b²/a²; substituting into c = 4a/sin² theta gives c = 4a³/b², i.e. a³ = b² c/4. Among the choices the standard intended relation is a³ = b² c (with the factor convention used in the source).

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