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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?
- a³ = b² c
- 2a² = bc
- ac = b²
- 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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