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On the parabola y² = 8x, a tangent and a normal are drawn at the point P(2, -4). They intersect the directrix of the parabola at points A and B respectively. If Q(a, b) is the point such that AQBP forms a square, find the value of 2a + b.
- -16
- -18
- -12
- -20
Correct answer: -16
Solution
A = (-2, 0) and B = (-2, -8); since PA and PB are perpendicular and equal, AQBP is a square whose diagonals PQ and AB bisect each other, giving Q = (-6, -4) and 2a + b = -16.
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