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From a point P(alpha, beta), two tangents are drawn touching the parabola y² = 8x at A and B, and the same point's tangents touch the ellipse x²/4 + y²/6 = 1 at C and D. Identify the correct relation(s)/value(s). (Multiple correct)

1. alpha + beta = -4
2. alpha*beta = 4
3. Area of triangle PAB is 128*sqrt(2)
4. Area of triangle PAB is 32*sqrt(2)

Correct answer: Area of triangle PAB is 32*sqrt(2)

Solution

Matching the chord of contact for both conics fixes P, and the area of triangle PAB (formed with the parabola tangents) works out to 32*sqrt(2).

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