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Two circles touch the parabola y² = 4x at the point (1, 2) and are also tangent to the x-axis. Find the area (in square units) of the smaller of these two circles.

1. 8*pi*(3 - 2*sqrt(2))
2. 4*pi*(2 - sqrt(2))
3. 4*pi*(3 + sqrt(2))
4. 8*pi*(2 - sqrt(2))

Correct answer: 8*pi*(3 - 2*sqrt(2))

Solution

Solving the tangency conditions gives two radii; the smaller circle has radius r with r² = 8(3 - 2*sqrt(2)), so its area is pi*r² = 8*pi*(3 - 2*sqrt(2)).

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