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Area Under the Curve
Area Between Two Curves
Premium Question
Grade 12

Question:

The area of the smaller region bounded by the ellipse $\frac{x^2}{9} + \frac{y^2}{4} = 1$ and the line $\frac{x}{3} + \frac{y}{2} = 1$ is:
(1) $\frac{3\pi}{2} - 3$
(2) $3\pi - 3$
(3) $\frac{3\pi}{2} - 6$
(4) $\frac{\pi}{2} - 3$

Step-by-Step Solution

Key Concept: Recognise the smaller region as the part of the first-quadrant quarter of the ellipse lying above the chord joining $(3, 0)$ and $(0, 2)$, and subtract the area of the triangle from the area of the quarter-ellipse.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (1)

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