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Find the equation of a common tangent to the parabola y² = 4x and the rectangular hyperbola xy = 2.
- x + 2y + 4 = 0
- x - 2y + 4 = 0
- x + y + 1 = 0
- 4x + 2y + 1 = 0
Correct answer: x + 2y + 4 = 0
Solution
Imposing tangency on xy = 2 gives m³ = -1/8, so m = -1/2 and the tangent y = -x/2 - 2 simplifies to x + 2y + 4 = 0.
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