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PQ is a focal chord of the parabola y² = 4ax. The tangents drawn at P and Q intersect at a point that lies on the line y = 2x + a (with a > 0). Find the length of the chord PQ.
- 5a
- 7a
- 2a
- 3a
Correct answer: 5a
Solution
The point of intersection of tangents at the ends of a focal chord lies on the directrix; using the given line gives t1+t2, and PQ length = a(t1-t2)²... actually focal chord length = a(t1 - t2)² with t1 t2 = -1.
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