The area of the region bounded by the ellipse x²/a² + y²/b² = 1 is:

Model Answer & Options

Source: Extra Practice

πab sq. units

2πab sq. units

πa²b² sq. units

π(a+b) sq. units

Explanation

The area is 4 times the area in the first quadrant: 4 * ∫[0 to a] (b/a)√(a² - x²) dx. Factoring out (b/a), the integral ∫[0 to a] √(a² - x²) dx equals πa²/4. Thus, Area = 4 * (b/a) * (πa²/4) = πab. Options B, C, and D are incorrect formulas for the area of an ellipse.

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