The area bounded by the ellipse `x^(2)/4 + y^(2)/25 = 1` is

Options

A. `2 pi sq. units`
B. `5 pi sq. units`
C. `20 pi sq. units`
D. `10 pi sq. units`

Answer

To find the area bounded by the ellipse given by the equation

\[ \frac{x^2}{4} + \frac{y^2}{25} = 1, \]

we can follow these steps:

### Step 1: Identify the semi-major and semi-minor axes
The standard form of the ellipse is

\[ \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1, \]

where \(a\) is the semi-minor axis and \(b\) is the semi-major axis. From the given equation, we can identify:

- \(a^2 = 4 \Rightarrow a = 2\)
- \(b^2 = 25 \Rightarrow b = 5\)

### Step 2: Use the formula for the area of an ellipse
The area \(A\) of an ellipse is given by the formula:

\[ A = \pi a b. \]

### Step 3: Substitute the values of \(a\) and \(b\)
Now substitute \(a = 2\) and \(b = 5\) into the area formula:

\[ A = \pi \times 2 \times 5 = 10\pi. \]

### Conclusion
Thus, the area bounded by the ellipse is

\[ \boxed{10\pi} \text{ square units.} \]

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