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Let curve C be the reflection of the parabola y² = 4x in the line x + y + 4 = 0. If A and B are the points where C meets the line y = -5, find the distance AB.

1. 4
2. 2 sqrt(5)
3. sqrt(77)
4. 6

Correct answer: 4

Solution

Reflecting points (t², 2t) of the parabola in x+y+4=0 gives (-2t-4, -t²-4). Setting -t²-4 = -5 gives t = ±1, and the corresponding x-values are -6 and -2, so AB = |-6 - (-2)| = 4.

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