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A parabola has its vertex at (1/2, 3/4) and directrix y = 1/2. Let P be the point where this parabola intersects the vertical line x = -1/2. The normal to the parabola drawn at P meets the parabola again at a point Q. Find (PQ)².
- 75/8
- 125/16
- 25/2
- 15/2
Correct answer: 125/16
Solution
With focus at (1/2, 1) and directrix y = 1/2, the parabola is (x-1/2)² = y - 3/4 (parameter 4a=1). At x=-1/2 we get P=(-1/2, 7/4). The normal has slope 1/2 and meets the parabola again at Q=(2, 3), giving (PQ)² = (5/2)² + (5/4)² = 125/16.
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