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Find the equations of the common tangents to the parabola y² = 4x and the ellipse x²/4 + y²/3 = 1.

1. x + 2y + 4 = 0 and x - 2y + 4 = 0
2. 2x - y + 1 = 0 and 2x + y + 1 = 0
3. x + y + 1 = 0 and x - y + 1 = 0
4. y = x + 1 and y = -x - 1

Correct answer: x + 2y + 4 = 0 and x - 2y + 4 = 0

Solution

Setting 1/m² = 4 m² + 3 gives m² = 1/4, so m = +-1/2 and c = +-2, producing the common tangents x - 2y + 4 = 0 and x + 2y + 4 = 0.

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