What is the area of the region bounded by the parabola y² = 4ax and its latus rectum?

Model Answer & Options

Source: Extra Practice

4a²/3 sq. units

8a²/3 sq. units

2a²/3 sq. units

16a²/3 sq. units

Explanation

The latus rectum of y² = 4ax is the line x = a. The area is symmetric about the x-axis, so we calculate the area above the axis and multiply by 2. Area = 2 * ∫[0 to a] √(4ax) dx = 4√a * ∫[0 to a] x^(1/2) dx = 4√a * [x^(3/2) / (3/2)] from 0 to a = 4√a * (2/3) * a^(3/2) = 8a²/3. Options A, C, and D represent common errors in neglecting symmetry or integration constants.

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