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Find the equation of the common tangent (lying above the x-axis) that touches both the circle (x - 3)² + y² = 9 and the parabola y² = 4x.
- sqrt(3)*y = x + 3
- sqrt(3)*y = 3x + 1
- sqrt(3)*y = -(x + 3)
- sqrt(3)*y = -(3x + 1)
Correct answer: sqrt(3)*y = x + 3
Solution
Using the parabola tangent y = mx + 1/m and the tangency condition to the circle gives m = 1/sqrt(3), so the tangent is y = x/sqrt(3) + sqrt(3), i.e. sqrt(3)y = x + 3.
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