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Find the set of all real values of m such that the two points P and Q lie on the line y = mx + 8 and satisfy ∠APB = ∠AQB = π/2, where A = (-4, 0) and B = (4, 0).

1. (-∞, -√3) ∪ (√3, ∞) {-2, 2}
2. [-√3, -√3] {-2, 2}
3. (-∞, -1) ∪ (1, ∞) {-2, 2}
4. {-√3, √3}

Correct answer: (-∞, -√3) ∪ (√3, ∞) {-2, 2}

Solution

The correct option identifies the slopes of the line formed by points P and Q that create right angles with the line segment AB. The conditions for the angles being π/2 lead to restrictions on the slope m, specifically excluding values between -√3 and √3, as well as the slopes -2 and 2, which correspond to the perpendicularity condition.

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