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The ellipse x²/9 + y²/5 = 1 has foci (f1, 0) and (f2, 0) with f1 > 0 > f2. Parabolas P1 and P2 share the vertex (0, 0) and have foci at (f1, 0) and (2*f2, 0) respectively. T1 is a tangent to P1 through (2*f2, 0), and T2 is a tangent to P2 through (f1, 0). If m1 and m2 are the slopes of T1 and T2, find the value of (1/m1²) + m2².
- 4
- 2
- 1
- 8
Correct answer: 4
Solution
With f1 = 2, f2 = -2, both parabolas have focal length 2 (P1: y² = 8x; P2: y² = -16x), and the tangent slope conditions give 1/m1² + m2² = 4.
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