Step 1: Understanding the Concept:
The standard equation of an ellipse is $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$. The total area is $\pi ab$. Since we only need the first quadrant, we take $1/4$ of the total area. Step 2: Formula Application:
Divide the given equation $4x^2 + 9y^2 = 144$ by 144:
$$\frac{4x^2}{144} + \frac{9y^2}{144} = 1 \implies \frac{x^2}{36} + \frac{y^2}{16} = 1$$
Here, $a^2 = 36 \implies a = 6$ and $b^2 = 16 \implies b = 4$. Step 3: Explanation:
Total Area = $\pi \times 6 \times 4 = 24\pi$.
Area in the first quadrant = $\frac{1}{4} \times 24\pi = 6\pi$. Step 4: Final Answer:
The area is $6\pi$.