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The line x - 2y + 4 = 0 is a common tangent to the parabola y² = 4x and the ellipse x²/4 + y²/b² = 1. Find the value of b and the equation of the other common tangent.
- b = sqrt(3); x + 2y + 4 = 0
- b = 3; x + 2y + 4 = 0
- b = sqrt(3); x + 2y - 4 = 0
- b = sqrt(3); x - 2y - 4 = 0
Correct answer: b = sqrt(3); x + 2y + 4 = 0
Solution
From y = x/2 + 2, the ellipse tangency c² = a² m² + b² gives 4 = 4*(1/4) + b², so b² = 3, b = sqrt(3); reflecting in the x-axis gives the second tangent x + 2y + 4 = 0.
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