Question

The area of the region bounded by the ellipse \[ \frac{x^2}{16} + \frac{y^2}{9} = 1 \] is:

• A. \( 12\pi \)
• B. \( 3\pi \)
• C. \( 24\pi \)
• D. \( \pi \)

Hint:

The area of an ellipse is \( \pi a b \), where \( a \) and \( b \) are the semi-major and semi-minor axes.

Answer 1

The Correct Option is A

Step 1: Using the standard area formula for an ellipse. 
The area of an ellipse is given by: \[ A = \pi a b \] where \( a^2 = 16 \Rightarrow a = 4 \) and \( b^2 = 9 \Rightarrow b = 3 \). 
Step 2: Calculating the area. 
\[ A = \pi (4)(3) = 12\pi \] Thus, the correct answer is (A).