Question

What is the area of the region bounded by the ellipse $\frac{x^2}{4} + \frac{y^2}{9} = 1$ ?

• A. 6π sq. units
• B. 3/2π sq. units
• C. 4π sq. units
• D. 8π sq. units

Answer 1

Answer:

A. 6π sq. units

The area of the region bounded by the ellipse is $6\

• Identify semi-axes: From $\frac{x^2}{4} + \frac{y^2}{9} = 1$, we find $a = 2$ and $b = 3$.

• Apply formula: Use the ellipse area formula $\text{Area} = \pi a b$.

• Calculate total: Multiplying $\pi \times 2 \times 3$ results in $6\pi$.