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On the parabola y² = x with vertex V, points A and B are chosen such that the chords VA and VB are mutually perpendicular. If θ is the angle that chord VA makes with the axis of the parabola, find the ratio |VA|/|VB|.
- tan θ
- tan³ θ
- cot² θ
- cot³ θ
Correct answer: cot³ θ
Solution
With a point (t², t), the chord length from vertex = |t|*sqrt(t²+1) and the angle θ satisfies tan θ = 1/t; working through the perpendicular condition gives |VA|/|VB| = cot³ θ.
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